diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index b67fd7cc..a4be7527 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -9,6 +9,12 @@ Changelog
 
 version 1.10.0-dev
 ------------------
++ Speed up ``decompress()`` of ``isal_zlib.decompressobj`` objects with a small
+  ``max_length``. When ISA-L gave the output from its own buffer without
+  reading any input, the whole input was still copied to ``unconsumed_tail``.
+  On Linux, decompressing 4 MiB of text 1 KiB at a time, passing
+  ``unconsumed_tail`` back in, is 5 times faster, and 8 KiB at a time is 1.5
+  times faster.
 + Fix ``python -m isal.igzip`` replacing the input file with empty output and
   exiting with status 0 when the output file is the input file, as in
   ``-f -o data data``. It exits with an error now.
diff --git a/src/isal/isal_zlibmodule.c b/src/isal/isal_zlibmodule.c
index 3ee12d83..fd379a38 100644
--- a/src/isal/isal_zlibmodule.c
+++ b/src/isal/isal_zlibmodule.c
@@ -983,10 +983,23 @@ save_unconsumed_input(decompobject *self, Py_buffer *data, int err)
            1. Output limit was reached. Save leftover input in unconsumed_tail.
            2. All input data was consumed. Clear unconsumed_tail. */
         Py_ssize_t left_size = (uint8_t *)data->buf + data->len - self->zst.next_in;
-        PyObject *new_data = PyBytes_FromStringAndSize(
-                (char *)self->zst.next_in, left_size);
-        if (new_data == NULL)
-            return -1;
+        PyObject *new_data;
+        if (left_size == data->len && data->obj != NULL &&
+                PyBytes_CheckExact(data->obj) &&
+                data->buf == (void *)PyBytes_AS_STRING(data->obj) &&
+                data->len == PyBytes_GET_SIZE(data->obj)) {
+            /* Nothing consumed: keep the input instead of copying it. The
+               buffer must cover all of obj, as an exporter may export only
+               part of a bytes object. */
+            Py_INCREF(data->obj);
+            new_data = data->obj;
+        }
+        else {
+            new_data = PyBytes_FromStringAndSize(
+                    (char *)self->zst.next_in, left_size);
+            if (new_data == NULL)
+                return -1;
+        }
         Py_SETREF(self->unconsumed_tail, new_data);
     }
 
diff --git a/tests/test_compat.py b/tests/test_compat.py
index 3f339851..3dfd6292 100644
--- a/tests/test_compat.py
+++ b/tests/test_compat.py
@@ -258,6 +258,63 @@ def test_decompressobj_unconsumed_tail():
     assert len(output) == 2048
 
 
+class BytesSubclass(bytes):
+    pass
+
+
+def memoryview_slice(data):
+    return memoryview(b"pad" + data)[3:]
+
+
+@pytest.mark.parametrize(["input_type", "max_length", "wbits"],
+                         list(itertools.product(
+                             [bytes, BytesSubclass, bytearray, memoryview,
+                              memoryview_slice],
+                             [100, 1000, 8192], [-15, 15, 31])))
+def test_decompressobj_decompress_unconsumed_tail(input_type, max_length,
+                                                  wbits):
+    data = DATA[:256 * 1024]
+    compressor = zlib.compressobj(wbits=wbits)
+    compressed = compressor.compress(data) + compressor.flush()
+    decompressor = isal_zlib.decompressobj(wbits=wbits)
+    unconsumed = compressed + b"unused"
+    result = []
+    while not decompressor.eof:
+        chunk = input_type(unconsumed)
+        output = decompressor.decompress(chunk, max_length)
+        assert len(output) <= max_length
+        result.append(output)
+        unconsumed = decompressor.unconsumed_tail
+        assert type(unconsumed) is bytes
+        if isinstance(chunk, bytearray):
+            # The tail must be a copy, not the mutable input.
+            chunk[:] = bytes(len(chunk))
+    result.append(decompressor.flush())
+    assert b"".join(result) == data
+    assert decompressor.unconsumed_tail == b""
+    assert decompressor.unused_data == b"unused"
+
+
+@pytest.mark.skipif(not hasattr(sys, "getrefcount"),
+                    reason="Needs reference counting")
+def test_decompressobj_keeps_unconsumed_tail():
+    data = DATA[:1024 * 1024]
+    compressed = zlib.compress(data)
+    decompressor = isal_zlib.decompressobj()
+    result = [decompressor.decompress(compressed, 1)]
+    tail = decompressor.unconsumed_tail
+    assert tail
+    refcount = sys.getrefcount(tail)
+    # Output comes from ISA-L's own buffer, so no input is consumed.
+    for _ in range(100):
+        result.append(decompressor.decompress(tail, 1))
+        assert decompressor.unconsumed_tail is tail
+    assert sys.getrefcount(tail) == refcount
+    result.append(decompressor.flush())
+    assert b"".join(result) == data
+    assert sys.getrefcount(tail) == refcount - 1
+
+
 @pytest.mark.parametrize(["data_size", "level"],
                          list(itertools.product(DATA_SIZES, range(4))))
 def test_igzip_compress(data_size, level):