diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index e68a8e4..76712e3 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -12,6 +12,8 @@ version 0.5.0-dev
 + Wheels are now build for MacOS arm64 architectures.
 + Fix a bug where READ and WRITE in zlib_ng.gzip_ng were inconsistent with the
   values in gzip on Python 3.13
++ Small simplifications to the ``gzip_ng.compress`` and ``gzip_ng.decompress``
+  functions, which should lead to less overhead.
 
 version 0.4.3
 -----------------
diff --git a/src/zlib_ng/gzip_ng.py b/src/zlib_ng/gzip_ng.py
index 24b5512..f24bdbe 100644
--- a/src/zlib_ng/gzip_ng.py
+++ b/src/zlib_ng/gzip_ng.py
@@ -22,6 +22,7 @@
 import gzip
 import io
 import os
+import shutil
 import struct
 import sys
 import time
@@ -180,50 +181,27 @@ def write(self, data):
 _GzipNGReader = _GzipReader
 
 
-def _create_simple_gzip_header(compresslevel: int,
-                               mtime=None) -> bytes:
-    """
-    Write a simple gzip header with no extra fields.
-    :param compresslevel: Compresslevel used to determine the xfl bytes.
-    :param mtime: The mtime (must support conversion to a 32-bit integer).
-    :return: A bytes object representing the gzip header.
-    """
-    if mtime is None:
-        mtime = time.time()
-    if compresslevel == _COMPRESS_LEVEL_BEST:
-        xfl = 2
-    elif compresslevel == _COMPRESS_LEVEL_FAST:
-        xfl = 4
-    else:
-        xfl = 0
-    # Pack ID1 and ID2 magic bytes, method (8=deflate), header flags (no extra
-    # fields added to header), mtime, xfl and os (255 for unknown OS).
-    return struct.pack("<BBBBLBB", 0x1f, 0x8b, 8, 0, int(mtime), xfl, 255)
-
-
 def compress(data, compresslevel=_COMPRESS_LEVEL_BEST, *, mtime=None):
     """Compress data in one shot and return the compressed string.
     compresslevel sets the compression level in range of 0-9.
     mtime can be used to set the modification time. The modification time is
     set to the current time by default.
     """
-    if mtime == 0:
-        # Use zlib as it creates the header with 0 mtime by default.
-        # This is faster and with less overhead.
-        return zlib_ng.compress(data, level=compresslevel, wbits=31)
-    header = _create_simple_gzip_header(compresslevel, mtime)
-    trailer = struct.pack("<LL", zlib_ng.crc32(data), (len(data) & 0xffffffff))
-    # Wbits=-15 creates a raw deflate block.
-    return (header + zlib_ng.compress(data, level=compresslevel, wbits=-15) +
-            trailer)
+    # Wbits=31 automatically includes a gzip header and trailer.
+    gzip_data = zlib_ng.compress(data, level=compresslevel, wbits=31)
+    if mtime is None:
+        mtime = time.time()
+    # Reuse gzip header created by zlib_ng, replace mtime and OS byte for
+    # consistency.
+    header = struct.pack("<4sLBB", gzip_data, int(mtime), gzip_data[8], 255)
+    return header + gzip_data[10:]
 
 
 def decompress(data):
     """Decompress a gzip compressed string in one shot.
     Return the decompressed string.
     """
-    fp = io.BytesIO(data)
-    reader = _GzipReader(fp, max(len(data), 16))
+    reader = _GzipReader(data)
     return reader.readall()
 
 
@@ -325,11 +303,7 @@ def main():
     global READ_BUFFER_SIZE
     READ_BUFFER_SIZE = args.buffer_size
     try:
-        while True:
-            block = in_file.read(args.buffer_size)
-            if block == b"":
-                break
-            out_file.write(block)
+        shutil.copyfileobj(in_file, out_file, args.buffer_size)
     finally:
         if in_file is not sys.stdin.buffer:
             in_file.close()