diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 1fb79cb4..8e90e3fe 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -55,6 +55,11 @@ version 1.8.1-dev
   input buffer when ``max_length`` split the end of a stream. At the end of a
   stream, ``isal_zlib.Decompress.unconsumed_tail`` is empty, matching the
   CPython fix for gh-158169.
++ Fix ``igzip_lib.IgzipDecompressor.needs_input``, which could be ``True``
+  after ``decompress()`` returned ``max_length`` bytes while more output was
+  still available. Readers that stop at the end of the file when
+  ``needs_input`` is ``True``, such as CPython's ``DecompressReader``, raised
+  ``EOFError`` for valid data.
 + Fix ``isal_zlib.decompressobj`` with a ``wbits`` of 40 to 47, which detects
   zlib or gzip data. It failed on gzip data when the first ``decompress()``
   call got fewer than 2 bytes, for example, when the data arrived byte by
diff --git a/src/isal/igzip_libmodule.c b/src/isal/igzip_libmodule.c
index 0f5779f0..d2896bb3 100644
--- a/src/isal/igzip_libmodule.c
+++ b/src/isal/igzip_libmodule.c
@@ -260,7 +260,11 @@ decompress(IgzipDecompressor *self, uint8_t *data, size_t len, Py_ssize_t max_le
     }
     else if (self->avail_in_real == 0) {
         self->state.next_in = NULL;
-        self->needs_input = 1;
+        /* When the output is full, isal_inflate can still read all of the
+           input and keep the decompressed data in its own buffer. Ask for
+           more input only when the output was not full, like CPython's
+           LZMADecompressor does. */
+        self->needs_input = (self->state.avail_out != 0);
     }
     else {
         self->needs_input = 0;
diff --git a/tests/test_igzip_lib.py b/tests/test_igzip_lib.py
index f2ccce1b..963d135f 100644
--- a/tests/test_igzip_lib.py
+++ b/tests/test_igzip_lib.py
@@ -284,6 +284,20 @@ def test_igzip_decompressor_unused_data_after_max_length(flag, wbits):
         assert decompressor.unused_data == compressed[stream_end:position]
 
 
+@pytest.mark.parametrize("max_length", [100, 8192])
+def test_igzip_decompressor_needs_input_after_all_input_is_read(max_length):
+    # When the output is full, ISA-L can read all of the input and keep the
+    # decompressed data in its own buffer. needs_input must stay False until
+    # decompress() has returned that data.
+    compressed = igzip_lib.compress(DATA)
+    decompressor = IgzipDecompressor()
+    result = [decompressor.decompress(compressed, max_length)]
+    while not decompressor.eof:
+        assert not decompressor.needs_input
+        result.append(decompressor.decompress(b"", max_length))
+    assert b"".join(result) == DATA
+
+
 @pytest.mark.skipif(not hasattr(sys, "getrefcount"),
                     reason="Needs reference counting")
 def test_igzip_decompressor_keeps_zdict_reference():