diff --git a/ext/zlib/zlib.c b/ext/zlib/zlib.c
index 982933b..0163129 100644
--- a/ext/zlib/zlib.c
+++ b/ext/zlib/zlib.c
@@ -434,7 +434,9 @@ do_checksum(int argc, VALUE *argv, checksum_func func)
     }
 
     if (NIL_P(str)) {
-	sum = func(mask32(sum), Z_NULL, 0);
+	/* zlib returns the initial value for a NULL buffer, which would discard
+	 * an explicitly given running checksum; behave like an empty string */
+	sum = NIL_P(vsum) ? func(0, Z_NULL, 0) : func(mask32(sum), (const Bytef *)"", 0);
     }
     else if (rb_obj_is_kind_of(str, rb_cIO)) {
         VALUE buf;
diff --git a/test/zlib/test_zlib.rb b/test/zlib/test_zlib.rb
index 1f9cb81..efacd24 100644
--- a/test/zlib/test_zlib.rb
+++ b/test/zlib/test_zlib.rb
@@ -1647,6 +1647,15 @@ def test_crc32_combine
       end
     end
 
+    def test_checksum_nil_with_initial_value
+      assert_equal(Zlib.crc32("", 1234), Zlib.crc32(nil, 1234))
+      assert_equal(1234, Zlib.crc32(nil, 1234))       # was 0
+      assert_equal(1234, Zlib.adler32(nil, 1234))     # was 1
+      assert_equal(Zlib.adler32("", 2**31 - 1), Zlib.adler32(nil, 2**31 - 1))
+      assert_equal(0, Zlib.crc32(nil))
+      assert_equal(1, Zlib.adler32(nil))
+    end
+
     def test_crc_table
       t = Zlib.crc_table
       assert_instance_of(Array, t)