diff --git a/config/libelf.pc.in b/config/libelf.pc.in
index 48f3f021..0d2ce968 100644
--- a/config/libelf.pc.in
+++ b/config/libelf.pc.in
@@ -11,4 +11,4 @@ URL: http://elfutils.org/
 Libs: -L${libdir} -lelf
 Cflags: -I${includedir}
 
-Requires.private: zlib
+Requires.private: zlib @LIBZSTD@
diff --git a/configure.ac b/configure.ac
index 59be27ac..ef16f79e 100644
--- a/configure.ac
+++ b/configure.ac
@@ -417,9 +417,11 @@ AC_SUBST([BZ2_LIB])
 eu_ZIPLIB(lzma,LZMA,lzma,lzma_auto_decoder,[LZMA (xz)])
 AS_IF([test "x$with_lzma" = xyes], [LIBLZMA="liblzma"], [LIBLZMA=""])
 AC_SUBST([LIBLZMA])
-eu_ZIPLIB(zstd,ZSTD,zstd,ZSTD_decompress,[ZSTD (zst)])
+eu_ZIPLIB(zstd,ZSTD,zstd,ZSTD_compressStream2,[ZSTD (zst)])
 AS_IF([test "x$with_zstd" = xyes], [LIBZSTD="libzstd"], [LIBLZSTD=""])
 AC_SUBST([LIBZSTD])
+zstd_LIBS="$LIBS"
+AC_SUBST([zstd_LIBS])
 zip_LIBS="$LIBS"
 LIBS="$save_LIBS"
 AC_SUBST([zip_LIBS])
diff --git a/libelf/Makefile.am b/libelf/Makefile.am
index 560ed45f..24c25cf8 100644
--- a/libelf/Makefile.am
+++ b/libelf/Makefile.am
@@ -106,7 +106,7 @@ libelf_pic_a_SOURCES =
 am_libelf_pic_a_OBJECTS = $(libelf_a_SOURCES:.c=.os)
 
 libelf_so_DEPS = ../lib/libeu.a
-libelf_so_LDLIBS = $(libelf_so_DEPS) -lz
+libelf_so_LDLIBS = $(libelf_so_DEPS) -lz $(zstd_LIBS)
 if USE_LOCKS
 libelf_so_LDLIBS += -lpthread
 endif
diff --git a/libelf/elf_compress.c b/libelf/elf_compress.c
index d7f53af2..deb585b7 100644
--- a/libelf/elf_compress.c
+++ b/libelf/elf_compress.c
@@ -39,6 +39,10 @@
 #include <string.h>
 #include <zlib.h>
 
+#ifdef USE_ZSTD
+#include <zstd.h>
+#endif
+
 /* Cleanup and return result.  Don't leak memory.  */
 static void *
 do_deflate_cleanup (void *result, z_stream *z, void *out_buf,
@@ -54,53 +58,14 @@ do_deflate_cleanup (void *result, z_stream *z, void *out_buf,
 #define deflate_cleanup(result, cdata) \
     do_deflate_cleanup(result, &z, out_buf, cdata)
 
-/* Given a section, uses the (in-memory) Elf_Data to extract the
-   original data size (including the given header size) and data
-   alignment.  Returns a buffer that has at least hsize bytes (for the
-   caller to fill in with a header) plus zlib compressed date.  Also
-   returns the new buffer size in new_size (hsize + compressed data
-   size).  Returns (void *) -1 when FORCE is false and the compressed
-   data would be bigger than the original data.  */
 void *
 internal_function
-__libelf_compress (Elf_Scn *scn, size_t hsize, int ei_data,
-		   size_t *orig_size, size_t *orig_addralign,
-		   size_t *new_size, bool force)
+__libelf_compress_zlib (Elf_Scn *scn, size_t hsize, int ei_data,
+			size_t *orig_size, size_t *orig_addralign,
+			size_t *new_size, bool force,
+			Elf_Data *data, Elf_Data *next_data,
+			void *out_buf, size_t out_size, size_t block)
 {
-  /* The compressed data is the on-disk data.  We simplify the
-     implementation a bit by asking for the (converted) in-memory
-     data (which might be all there is if the user created it with
-     elf_newdata) and then convert back to raw if needed before
-     compressing.  Should be made a bit more clever to directly
-     use raw if that is directly available.  */
-  Elf_Data *data = elf_getdata (scn, NULL);
-  if (data == NULL)
-    return NULL;
-
-  /* When not forced and we immediately know we would use more data by
-     compressing, because of the header plus zlib overhead (five bytes
-     per 16 KB block, plus a one-time overhead of six bytes for the
-     entire stream), don't do anything.  */
-  Elf_Data *next_data = elf_getdata (scn, data);
-  if (next_data == NULL && !force
-      && data->d_size <= hsize + 5 + 6)
-    return (void *) -1;
-
-  *orig_addralign = data->d_align;
-  *orig_size = data->d_size;
-
-  /* Guess an output block size. 1/8th of the original Elf_Data plus
-     hsize.  Make the first chunk twice that size (25%), then increase
-     by a block (12.5%) when necessary.  */
-  size_t block = (data->d_size / 8) + hsize;
-  size_t out_size = 2 * block;
-  void *out_buf = malloc (out_size);
-  if (out_buf == NULL)
-    {
-      __libelf_seterrno (ELF_E_NOMEM);
-      return NULL;
-    }
-
   /* Caller gets to fill in the header at the start.  Just skip it here.  */
   size_t used = hsize;
 
@@ -205,9 +170,189 @@ __libelf_compress (Elf_Scn *scn, size_t hsize, int ei_data,
   return out_buf;
 }
 
+#ifdef USE_ZSTD
+/* Cleanup and return result.  Don't leak memory.  */
+static void *
+do_zstd_cleanup (void *result, ZSTD_CCtx * const cctx, void *out_buf,
+		 Elf_Data *cdatap)
+{
+  ZSTD_freeCCtx (cctx);
+  free (out_buf);
+  if (cdatap != NULL)
+    free (cdatap->d_buf);
+  return result;
+}
+
+#define zstd_cleanup(result, cdata) \
+    do_zstd_cleanup(result, cctx, out_buf, cdata)
+
+void *
+internal_function
+__libelf_compress_zstd (Elf_Scn *scn, size_t hsize, int ei_data,
+			size_t *orig_size, size_t *orig_addralign,
+			size_t *new_size, bool force,
+			Elf_Data *data, Elf_Data *next_data,
+			void *out_buf, size_t out_size, size_t block)
+{
+  /* Caller gets to fill in the header at the start.  Just skip it here.  */
+  size_t used = hsize;
+
+  ZSTD_CCtx* const cctx = ZSTD_createCCtx();
+  Elf_Data cdata;
+  cdata.d_buf = NULL;
+
+  /* Loop over data buffers.  */
+  ZSTD_EndDirective mode = ZSTD_e_continue;
+
+  do
+    {
+      /* Convert to raw if different endianness.  */
+      cdata = *data;
+      bool convert = ei_data != MY_ELFDATA && data->d_size > 0;
+      if (convert)
+	{
+	  /* Don't do this conversion in place, we might want to keep
+	     the original data around, caller decides.  */
+	  cdata.d_buf = malloc (data->d_size);
+	  if (cdata.d_buf == NULL)
+	    {
+	      __libelf_seterrno (ELF_E_NOMEM);
+	      return zstd_cleanup (NULL, NULL);
+	    }
+	  if (gelf_xlatetof (scn->elf, &cdata, data, ei_data) == NULL)
+	    return zstd_cleanup (NULL, &cdata);
+	}
+
+      ZSTD_inBuffer ib = { cdata.d_buf, cdata.d_size, 0 };
+
+      /* Get next buffer to see if this is the last one.  */
+      data = next_data;
+      if (data != NULL)
+	{
+	  *orig_addralign = MAX (*orig_addralign, data->d_align);
+	  *orig_size += data->d_size;
+	  next_data = elf_getdata (scn, data);
+	}
+      else
+	mode = ZSTD_e_end;
+
+      /* Flush one data buffer.  */
+      for (;;)
+	{
+	  ZSTD_outBuffer ob = { out_buf + used, out_size - used, 0 };
+	  size_t ret = ZSTD_compressStream2 (cctx, &ob, &ib, mode);
+	  if (ZSTD_isError (ret))
+	    {
+	      __libelf_seterrno (ELF_E_COMPRESS_ERROR);
+	      return zstd_cleanup (NULL, convert ? &cdata : NULL);
+	    }
+	  used += ob.pos;
+
+	  /* Bail out if we are sure the user doesn't want the
+	     compression forced and we are using more compressed data
+	     than original data.  */
+	  if (!force && mode == ZSTD_e_end && used >= *orig_size)
+	    return zstd_cleanup ((void *) -1, convert ? &cdata : NULL);
+
+	  if (ret > 0)
+	    {
+	      void *bigger = realloc (out_buf, out_size + block);
+	      if (bigger == NULL)
+		{
+		  __libelf_seterrno (ELF_E_NOMEM);
+		  return zstd_cleanup (NULL, convert ? &cdata : NULL);
+		}
+	      out_buf = bigger;
+	      out_size += block;
+	    }
+	  else
+	    break;
+	}
+
+      if (convert)
+	{
+	  free (cdata.d_buf);
+	  cdata.d_buf = NULL;
+	}
+    }
+  while (mode != ZSTD_e_end); /* More data blocks.  */
+
+  ZSTD_freeCCtx (cctx);
+  *new_size = used;
+  return out_buf;
+}
+#endif
+
+/* Given a section, uses the (in-memory) Elf_Data to extract the
+   original data size (including the given header size) and data
+   alignment.  Returns a buffer that has at least hsize bytes (for the
+   caller to fill in with a header) plus zlib compressed date.  Also
+   returns the new buffer size in new_size (hsize + compressed data
+   size).  Returns (void *) -1 when FORCE is false and the compressed
+   data would be bigger than the original data.  */
+void *
+internal_function
+__libelf_compress (Elf_Scn *scn, size_t hsize, int ei_data,
+		   size_t *orig_size, size_t *orig_addralign,
+		   size_t *new_size, bool force, bool use_zstd)
+{
+  /* The compressed data is the on-disk data.  We simplify the
+     implementation a bit by asking for the (converted) in-memory
+     data (which might be all there is if the user created it with
+     elf_newdata) and then convert back to raw if needed before
+     compressing.  Should be made a bit more clever to directly
+     use raw if that is directly available.  */
+  Elf_Data *data = elf_getdata (scn, NULL);
+  if (data == NULL)
+    return NULL;
+
+  /* When not forced and we immediately know we would use more data by
+     compressing, because of the header plus zlib overhead (five bytes
+     per 16 KB block, plus a one-time overhead of six bytes for the
+     entire stream), don't do anything.
+     Size estimation for ZSTD compression would be similar.  */
+  Elf_Data *next_data = elf_getdata (scn, data);
+  if (next_data == NULL && !force
+      && data->d_size <= hsize + 5 + 6)
+    return (void *) -1;
+
+  *orig_addralign = data->d_align;
+  *orig_size = data->d_size;
+
+  /* Guess an output block size. 1/8th of the original Elf_Data plus
+     hsize.  Make the first chunk twice that size (25%), then increase
+     by a block (12.5%) when necessary.  */
+  size_t block = (data->d_size / 8) + hsize;
+  size_t out_size = 2 * block;
+  void *out_buf = malloc (out_size);
+  if (out_buf == NULL)
+    {
+      __libelf_seterrno (ELF_E_NOMEM);
+      return NULL;
+    }
+
+  if (use_zstd)
+    {
+#ifdef USE_ZSTD
+      return __libelf_compress_zstd (scn, hsize, ei_data, orig_size,
+				   orig_addralign, new_size, force,
+				   data, next_data, out_buf, out_size,
+				   block);
+#else
+    __libelf_seterrno (ELF_E_UNKNOWN_COMPRESSION_TYPE);
+    return NULL;
+#endif
+    }
+  else
+    return __libelf_compress_zlib (scn, hsize, ei_data, orig_size,
+				   orig_addralign, new_size, force,
+				   data, next_data, out_buf, out_size,
+				   block);
+}
+
 void *
 internal_function
-__libelf_decompress (void *buf_in, size_t size_in, size_t size_out)
+__libelf_decompress_zlib (void *buf_in, size_t size_in, size_t size_out)
 {
   /* Catch highly unlikely compression ratios so we don't allocate
      some giant amount of memory for nothing. The max compression
@@ -218,7 +363,7 @@ __libelf_decompress (void *buf_in, size_t size_in, size_t size_out)
       return NULL;
     }
 
-  /* Malloc might return NULL when requestion zero size.  This is highly
+  /* Malloc might return NULL when requesting zero size.  This is highly
      unlikely, it would only happen when the compression was forced.
      But we do need a non-NULL buffer to return and set as result.
      Just make sure to always allocate at least 1 byte.  */
@@ -260,6 +405,51 @@ __libelf_decompress (void *buf_in, size_t size_in, size_t size_out)
   return buf_out;
 }
 
+#ifdef USE_ZSTD
+void *
+internal_function
+__libelf_decompress_zstd (void *buf_in, size_t size_in, size_t size_out)
+{
+  /* Malloc might return NULL when requesting zero size.  This is highly
+     unlikely, it would only happen when the compression was forced.
+     But we do need a non-NULL buffer to return and set as result.
+     Just make sure to always allocate at least 1 byte.  */
+  void *buf_out = malloc (size_out ?: 1);
+  if (unlikely (buf_out == NULL))
+    {
+      __libelf_seterrno (ELF_E_NOMEM);
+      return NULL;
+    }
+
+  size_t ret = ZSTD_decompress (buf_out, size_out, buf_in, size_in);
+  if (ZSTD_isError (ret))
+    {
+      free (buf_out);
+      __libelf_seterrno (ELF_E_UNKNOWN_COMPRESSION_TYPE);
+      return NULL;
+    }
+  else
+    return buf_out;
+}
+#endif
+
+void *
+internal_function
+__libelf_decompress (int chtype, void *buf_in, size_t size_in, size_t size_out)
+{
+  if (chtype == ELFCOMPRESS_ZLIB)
+    return __libelf_decompress_zlib (buf_in, size_in, size_out);
+  else
+    {
+#ifdef USE_ZSTD
+    return __libelf_decompress_zstd (buf_in, size_in, size_out);
+#else
+    __libelf_seterrno (ELF_E_DECOMPRESS_ERROR);
+    return NULL;
+#endif
+    }
+}
+
 void *
 internal_function
 __libelf_decompress_elf (Elf_Scn *scn, size_t *size_out, size_t *addralign)
@@ -268,7 +458,19 @@ __libelf_decompress_elf (Elf_Scn *scn, size_t *size_out, size_t *addralign)
   if (gelf_getchdr (scn, &chdr) == NULL)
     return NULL;
 
+  bool unknown_compression = false;
   if (chdr.ch_type != ELFCOMPRESS_ZLIB)
+    {
+      if (chdr.ch_type != ELFCOMPRESS_ZSTD)
+	unknown_compression = true;
+
+#ifndef USE_ZSTD
+      if (chdr.ch_type == ELFCOMPRESS_ZSTD)
+	unknown_compression = true;
+#endif
+    }
+
+  if (unknown_compression)
     {
       __libelf_seterrno (ELF_E_UNKNOWN_COMPRESSION_TYPE);
       return NULL;
@@ -295,7 +497,9 @@ __libelf_decompress_elf (Elf_Scn *scn, size_t *size_out, size_t *addralign)
 		  ? sizeof (Elf32_Chdr) : sizeof (Elf64_Chdr));
   size_t size_in = data->d_size - hsize;
   void *buf_in = data->d_buf + hsize;
-  void *buf_out = __libelf_decompress (buf_in, size_in, chdr.ch_size);
+  void *buf_out
+    = __libelf_decompress (chdr.ch_type, buf_in, size_in, chdr.ch_size);
+
   *size_out = chdr.ch_size;
   *addralign = chdr.ch_addralign;
   return buf_out;
@@ -394,7 +598,7 @@ elf_compress (Elf_Scn *scn, int type, unsigned int flags)
     }
 
   int compressed = (sh_flags & SHF_COMPRESSED);
-  if (type == ELFCOMPRESS_ZLIB)
+  if (type == ELFCOMPRESS_ZLIB || type == ELFCOMPRESS_ZSTD)
     {
       /* Compress/Deflate.  */
       if (compressed == 1)
@@ -408,7 +612,8 @@ elf_compress (Elf_Scn *scn, int type, unsigned int flags)
       size_t orig_size, orig_addralign, new_size;
       void *out_buf = __libelf_compress (scn, hsize, elfdata,
 					 &orig_size, &orig_addralign,
-					 &new_size, force);
+					 &new_size, force,
+					 type == ELFCOMPRESS_ZSTD);
 
       /* Compression would make section larger, don't change anything.  */
       if (out_buf == (void *) -1)
@@ -422,7 +627,7 @@ elf_compress (Elf_Scn *scn, int type, unsigned int flags)
       if (elfclass == ELFCLASS32)
 	{
 	  Elf32_Chdr chdr;
-	  chdr.ch_type = ELFCOMPRESS_ZLIB;
+	  chdr.ch_type = type;
 	  chdr.ch_size = orig_size;
 	  chdr.ch_addralign = orig_addralign;
 	  if (elfdata != MY_ELFDATA)
@@ -436,7 +641,7 @@ elf_compress (Elf_Scn *scn, int type, unsigned int flags)
       else
 	{
 	  Elf64_Chdr chdr;
-	  chdr.ch_type = ELFCOMPRESS_ZLIB;
+	  chdr.ch_type = type;
 	  chdr.ch_reserved = 0;
 	  chdr.ch_size = orig_size;
 	  chdr.ch_addralign = sh_addralign;
diff --git a/libelf/elf_compress_gnu.c b/libelf/elf_compress_gnu.c
index 3d2977e7..8e20b30e 100644
--- a/libelf/elf_compress_gnu.c
+++ b/libelf/elf_compress_gnu.c
@@ -103,7 +103,8 @@ elf_compress_gnu (Elf_Scn *scn, int inflate, unsigned int flags)
       size_t orig_size, new_size, orig_addralign;
       void *out_buf = __libelf_compress (scn, hsize, elfdata,
 					 &orig_size, &orig_addralign,
-					 &new_size, force);
+					 &new_size, force,
+					 /* use_zstd */ false);
 
       /* Compression would make section larger, don't change anything.  */
       if (out_buf == (void *) -1)
@@ -178,7 +179,7 @@ elf_compress_gnu (Elf_Scn *scn, int inflate, unsigned int flags)
       size_t size = gsize;
       size_t size_in = data->d_size - hsize;
       void *buf_in = data->d_buf + hsize;
-      void *buf_out = __libelf_decompress (buf_in, size_in, size);
+      void *buf_out = __libelf_decompress (ELFCOMPRESS_ZLIB, buf_in, size_in, size);
       if (buf_out == NULL)
 	return -1;
 
diff --git a/libelf/libelfP.h b/libelf/libelfP.h
index d88a613c..6624f38a 100644
--- a/libelf/libelfP.h
+++ b/libelf/libelfP.h
@@ -574,10 +574,10 @@ extern uint32_t __libelf_crc32 (uint32_t crc, unsigned char *buf, size_t len)
 
 extern void * __libelf_compress (Elf_Scn *scn, size_t hsize, int ei_data,
 				 size_t *orig_size, size_t *orig_addralign,
-				 size_t *size, bool force)
+				 size_t *size, bool force, bool use_zstd)
      internal_function;
 
-extern void * __libelf_decompress (void *buf_in, size_t size_in,
+extern void * __libelf_decompress (int chtype, void *buf_in, size_t size_in,
 				   size_t size_out) internal_function;
 extern void * __libelf_decompress_elf (Elf_Scn *scn,
 				       size_t *size_out, size_t *addralign)
diff --git a/src/elfcompress.c b/src/elfcompress.c
index eff765e8..bfdac2b4 100644
--- a/src/elfcompress.c
+++ b/src/elfcompress.c
@@ -55,9 +55,10 @@ enum ch_type
   UNSET = -1,
   NONE,
   ZLIB,
+  ZSTD,
 
   /* Maximal supported ch_type.  */
-  MAXIMAL_CH_TYPE = ZLIB,
+  MAXIMAL_CH_TYPE = ZSTD,
 
   ZLIB_GNU = 1 << 16
 };
@@ -139,6 +140,12 @@ parse_opt (int key, char *arg __attribute__ ((unused)),
 	type = ZLIB;
       else if (strcmp ("zlib-gnu", arg) == 0 || strcmp ("gnu", arg) == 0)
 	type = ZLIB_GNU;
+      else if (strcmp ("zstd", arg) == 0)
+#ifdef USE_ZSTD
+	type = ZSTD;
+#else
+	argp_error (state, N_("ZSTD support is not enabled"));
+#endif
       else
 	argp_error (state, N_("unknown compression type '%s'"), arg);
       break;
@@ -281,6 +288,44 @@ get_sections (unsigned int *sections, size_t shnum)
   return s;
 }
 
+/* Return compression type of a given section SHDR.  */
+
+static enum ch_type
+get_section_chtype (Elf_Scn *scn, GElf_Shdr *shdr, const char *sname,
+		    size_t ndx)
+{
+  enum ch_type chtype = UNSET;
+  if ((shdr->sh_flags & SHF_COMPRESSED) != 0)
+    {
+      GElf_Chdr chdr;
+      if (gelf_getchdr (scn, &chdr) != NULL)
+	{
+	  chtype = (enum ch_type)chdr.ch_type;
+	  if (chtype == NONE)
+	    {
+	      error (0, 0, "Compression type for section %zd"
+		     " can't be zero ", ndx);
+	      chtype = UNSET;
+	    }
+	  else if (chtype > MAXIMAL_CH_TYPE)
+	    {
+	      error (0, 0, "Compression type (%d) for section %zd"
+		     " is unsupported ", chtype, ndx);
+	      chtype = UNSET;
+	    }
+	}
+      else
+	error (0, 0, "Couldn't get chdr for section %zd", ndx);
+    }
+  /* Set ZLIB_GNU compression manually for .zdebug* sections.  */
+  else if (startswith (sname, ".zdebug"))
+    chtype = ZLIB_GNU;
+  else
+    chtype = NONE;
+
+  return chtype;
+}
+
 static int
 process_file (const char *fname)
 {
@@ -461,26 +506,29 @@ process_file (const char *fname)
 
       if (section_name_matches (sname))
 	{
-	  if (!force && type == NONE
-	      && (shdr->sh_flags & SHF_COMPRESSED) == 0
-	      && !startswith (sname, ".zdebug"))
-	    {
-	      if (verbose > 0)
-		printf ("[%zd] %s already decompressed\n", ndx, sname);
-	    }
-	  else if (!force && type == ZLIB
-		   && (shdr->sh_flags & SHF_COMPRESSED) != 0)
-	    {
-	      if (verbose > 0)
-		printf ("[%zd] %s already compressed\n", ndx, sname);
-	    }
-	  else if (!force && type == ZLIB_GNU
-		   && startswith (sname, ".zdebug"))
+	  enum ch_type schtype = get_section_chtype (scn, shdr, sname, ndx);
+	  if (!force && verbose > 0)
 	    {
-	      if (verbose > 0)
-		printf ("[%zd] %s already GNU compressed\n", ndx, sname);
+	      /* The current compression matches the final one.  */
+	      if (type == schtype)
+		switch (type)
+		  {
+		  case NONE:
+		    printf ("[%zd] %s already decompressed\n", ndx, sname);
+		    break;
+		  case ZLIB:
+		  case ZSTD:
+		    printf ("[%zd] %s already compressed\n", ndx, sname);
+		    break;
+		  case ZLIB_GNU:
+		    printf ("[%zd] %s already GNU compressed\n", ndx, sname);
+		    break;
+		  default:
+		    abort ();
+		  }
 	    }
-	  else if (shdr->sh_type != SHT_NOBITS
+
+	  if (shdr->sh_type != SHT_NOBITS
 	      && (shdr->sh_flags & SHF_ALLOC) == 0)
 	    {
 	      set_section (sections, ndx);
@@ -692,37 +740,12 @@ process_file (const char *fname)
 	     (de)compressed, invalidating the string pointers.  */
 	  sname = xstrdup (sname);
 
+
 	  /* Detect source compression that is how is the section compressed
 	     now.  */
-	  GElf_Chdr chdr;
-	  enum ch_type schtype = NONE;
-	  if ((shdr->sh_flags & SHF_COMPRESSED) != 0)
-	    {
-	      if (gelf_getchdr (scn, &chdr) != NULL)
-		{
-		  schtype = (enum ch_type)chdr.ch_type;
-		  if (schtype == NONE)
-		    {
-		      error (0, 0, "Compression type for section %zd"
-			     " can't be zero ", ndx);
-		      goto cleanup;
-		    }
-		  else if (schtype > MAXIMAL_CH_TYPE)
-		    {
-		      error (0, 0, "Compression type (%d) for section %zd"
-			     " is unsupported ", schtype, ndx);
-		      goto cleanup;
-		    }
-		}
-	      else
-		{
-		  error (0, 0, "Couldn't get chdr for section %zd", ndx);
-		  goto cleanup;
-		}
-	    }
-	  /* Set ZLIB compression manually for .zdebug* sections.  */
-	  else if (startswith (sname, ".zdebug"))
-	    schtype = ZLIB_GNU;
+	  enum ch_type schtype = get_section_chtype (scn, shdr, sname, ndx);
+	  if (schtype == UNSET)
+	    goto cleanup;
 
 	  /* We might want to decompress (and rename), but not
 	     compress during this pass since we might need the section
@@ -754,7 +777,7 @@ process_file (const char *fname)
 	    case ZLIB_GNU:
 	      if (startswith (sname, ".debug"))
 		{
-		  if (schtype == ZLIB)
+		  if (schtype == ZLIB || schtype == ZSTD)
 		    {
 		      /* First decompress to recompress GNU style.
 			 Don't report even when verbose.  */
@@ -818,19 +841,22 @@ process_file (const char *fname)
 	      break;
 
 	    case ZLIB:
-	      if ((shdr->sh_flags & SHF_COMPRESSED) == 0)
+	    case ZSTD:
+	      if (schtype != type)
 		{
-		  if (schtype == ZLIB_GNU)
+		  if (schtype != NONE)
 		    {
-		      /* First decompress to recompress zlib style.
-			 Don't report even when verbose.  */
+		      /* Decompress first.  */
 		      if (compress_section (scn, size, sname, NULL, ndx,
 					    schtype, NONE, false) < 0)
 			goto cleanup;
 
-		      snamebuf[0] = '.';
-		      strcpy (&snamebuf[1], &sname[2]);
-		      newname = snamebuf;
+		      if (schtype == ZLIB_GNU)
+			{
+			  snamebuf[0] = '.';
+			  strcpy (&snamebuf[1], &sname[2]);
+			  newname = snamebuf;
+			}
 		    }
 
 		  if (skip_compress_section)
@@ -838,7 +864,7 @@ process_file (const char *fname)
 		      if (ndx == shdrstrndx)
 			{
 			  shstrtab_size = size;
-			  shstrtab_compressed = ZLIB;
+			  shstrtab_compressed = type;
 			  if (shstrtab_name != NULL
 			      || shstrtab_newname != NULL)
 			    {
@@ -855,7 +881,7 @@ process_file (const char *fname)
 		      else
 			{
 			  symtab_size = size;
-			  symtab_compressed = ZLIB;
+			  symtab_compressed = type;
 			  symtab_name = xstrdup (sname);
 			  symtab_newname = (newname == NULL
 					    ? NULL : xstrdup (newname));
@@ -1378,7 +1404,8 @@ main (int argc, char **argv)
 	N_("Place (de)compressed output into FILE"),
 	0 },
       { "type", 't', "TYPE", 0,
-	N_("What type of compression to apply. TYPE can be 'none' (decompress), 'zlib' (ELF ZLIB compression, the default, 'zlib-gabi' is an alias) or 'zlib-gnu' (.zdebug GNU style compression, 'gnu' is an alias)"),
+	N_("What type of compression to apply. TYPE can be 'none' (decompress), 'zlib' (ELF ZLIB compression, the default, 'zlib-gabi' is an alias), "
+	   "'zlib-gnu' (.zdebug GNU style compression, 'gnu' is an alias) or 'zstd' (ELF ZSTD compression)"),
 	0 },
       { "name", 'n', "SECTION", 0,
 	N_("SECTION name to (de)compress, SECTION is an extended wildcard pattern (defaults to '.?(z)debug*')"),
diff --git a/src/readelf.c b/src/readelf.c
index cc3e0229..451f8400 100644
--- a/src/readelf.c
+++ b/src/readelf.c
@@ -1238,13 +1238,17 @@ get_visibility_type (int value)
 static const char *
 elf_ch_type_name (unsigned int code)
 {
-  if (code == 0)
-    return "NONE";
-
-  if (code == ELFCOMPRESS_ZLIB)
-    return "ZLIB";
-
-  return "UNKNOWN";
+  switch (code)
+    {
+    case 0:
+      return "NONE";
+    case ELFCOMPRESS_ZLIB:
+      return "ZLIB";
+    case ELFCOMPRESS_ZSTD:
+      return "ZSTD";
+    default:
+      return "UNKNOWN";
+    }
 }
 
 /* Print the section headers.  */
diff --git a/tests/Makefile.am b/tests/Makefile.am
index 356b3fbf..c1868307 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -218,6 +218,7 @@ endif
 
 if HAVE_ZSTD
 TESTS += run-readelf-compressed-zstd.sh
+export ELFUTILS_ZSTD = 1
 endif
 
 if DEBUGINFOD
diff --git a/tests/run-compress-test.sh b/tests/run-compress-test.sh
index a6a298f5..2d4eebd6 100755
--- a/tests/run-compress-test.sh
+++ b/tests/run-compress-test.sh
@@ -61,6 +61,34 @@ testrun_elfcompress_file()
     echo "uncompress $elfcompressedfile -> $elfuncompressedfile"
     testrun ${abs_top_builddir}/src/elfcompress -v -t none -o ${elfuncompressedfile} ${elfcompressedfile}
     testrun ${abs_top_builddir}/src/elfcmp ${uncompressedfile} ${elfuncompressedfile}
+
+    if test -z "$ELFUTILS_ZSTD"; then
+      return;
+    fi
+
+    outputfile="${infile}.gabi.zstd"
+    tempfiles "$outputfile"
+    echo "zstd compress $elfcompressedfile -> $outputfile"
+    testrun ${abs_top_builddir}/src/elfcompress -v -t zstd -o ${outputfile} ${elfcompressedfile}
+    testrun ${abs_top_builddir}/src/elfcmp ${uncompressedfile} ${outputfile}
+    echo "checking compressed section header" $outputfile
+    testrun ${abs_top_builddir}/src/readelf -Sz ${outputfile} | grep "ELF ZSTD" >/dev/null
+
+    zstdfile="${infile}.zstd"
+    tempfiles "$zstdfile"
+    echo "zstd compress $uncompressedfile -> $zstdfile"
+    testrun ${abs_top_builddir}/src/elfcompress -v -t zstd -o ${zstdfile} ${elfuncompressedfile}
+    testrun ${abs_top_builddir}/src/elfcmp ${uncompressedfile} ${zstdfile}
+    echo "checking compressed section header" $zstdfile
+    testrun ${abs_top_builddir}/src/readelf -Sz ${zstdfile} | grep "ELF ZSTD" >/dev/null
+
+    zstdgnufile="${infile}.zstd.gnu"
+    tempfiles "$zstdgnufile"
+    echo "zstd re-compress to GNU ZLIB $zstdfile -> $zstdgnufile"
+    testrun ${abs_top_builddir}/src/elfcompress -v -t zlib-gnu -o ${zstdgnufile} ${zstdfile}
+    testrun ${abs_top_builddir}/src/elfcmp ${uncompressedfile} ${zstdgnufile}
+    echo "checking .zdebug section name" $zstdgnufile
+    testrun ${abs_top_builddir}/src/readelf -S ${zstdgnufile} | grep ".zdebug" >/dev/null
 }
 
 testrun_elfcompress()
