diff --git a/av/container/output.py b/av/container/output.py
index 145437752..e57f269e8 100644
--- a/av/container/output.py
+++ b/av/container/output.py
@@ -278,15 +278,23 @@ def add_data_stream(self, codec_name=None, options: dict | None = None):
         :rtype: The new :class:`~av.data.stream.DataStream`.
         """
         codec: cython.pointer[cython.const[lib.AVCodec]] = cython.NULL
+        codec_descriptor: cython.pointer[lib.AVCodecDescriptor] = cython.NULL
 
         if codec_name is not None:
             codec = lib.avcodec_find_encoder_by_name(codec_name.encode())
             if codec == cython.NULL:
-                raise ValueError(f"Unknown data codec: {codec_name}")
+                codec = lib.avcodec_find_decoder_by_name(codec_name.encode())
+            if codec == cython.NULL:
+                codec_descriptor = lib.avcodec_descriptor_get_by_name(
+                    codec_name.encode()
+                )
+                if codec_descriptor == cython.NULL:
+                    raise ValueError(f"Unknown data codec: {codec_name}")
 
-            # Assert that this format supports the requested codec
+            # Verify format supports this codec
+            codec_id = codec.id if codec != cython.NULL else codec_descriptor.id
             if not lib.avformat_query_codec(
-                self.ptr.oformat, codec.id, lib.FF_COMPLIANCE_NORMAL
+                self.ptr.oformat, codec_id, lib.FF_COMPLIANCE_NORMAL
             ):
                 raise ValueError(
                     f"{self.format.name!r} format does not support {codec_name!r} codec"
@@ -297,7 +305,7 @@ def add_data_stream(self, codec_name=None, options: dict | None = None):
         if stream == cython.NULL:
             raise MemoryError("Could not allocate stream")
 
-        # Set up codec context if we have a codec
+        # Set up codec context and parameters
         ctx: cython.pointer[lib.AVCodecContext] = cython.NULL
         if codec != cython.NULL:
             ctx = lib.avcodec_alloc_context3(codec)
@@ -311,8 +319,10 @@ def add_data_stream(self, codec_name=None, options: dict | None = None):
             # Initialize stream codec parameters
             err_check(lib.avcodec_parameters_from_context(stream.codecpar, ctx))
         else:
-            # For raw data streams, just set the codec type
+            # No codec available - set basic parameters for data stream
             stream.codecpar.codec_type = lib.AVMEDIA_TYPE_DATA
+            if codec_descriptor != cython.NULL:
+                stream.codecpar.codec_id = codec_descriptor.id
 
         # Construct the user-land stream
         py_codec_context: CodecContext | None = None
diff --git a/tests/test_streams.py b/tests/test_streams.py
index f82ce384b..9387d68cc 100644
--- a/tests/test_streams.py
+++ b/tests/test_streams.py
@@ -17,6 +17,8 @@ def cleanup(self):
             "data.ts",
             "data_source.ts",
             "data_copy.ts",
+            "data_with_codec.ts",
+            "data_invalid.ts",
             "out.mkv",
             "video_with_attachment.mkv",
             "remuxed_attachment.mkv",
@@ -201,6 +203,50 @@ def test_data_stream_from_template(self) -> None:
 
         assert remuxed_payloads == copied_payloads
 
+    def test_data_stream_with_codec(self) -> None:
+        """Test adding a data stream with a specific codec name."""
+        # Test that invalid codec names raise appropriate errors
+        with pytest.raises(ValueError, match="Unknown data codec"):
+            container = av.open("data_invalid.ts", "w")
+            try:
+                container.add_data_stream("not_a_real_codec_name_12345")
+            finally:
+                container.close()
+
+        # Test that add_data_stream with codec parameter works correctly
+        # We use "bin_data" which is a data codec that's always available
+        output_path = "data_with_codec.ts"
+        with av.open(output_path, "w") as container:
+            # Try to create a data stream with a codec
+            # bin_data is a simple passthrough codec for binary data
+            data_stream = container.add_data_stream("bin_data")
+            klv_stream = container.add_data_stream("klv")
+
+            assert data_stream.type == "data"
+            assert klv_stream.type == "data"
+            # Note: codec_context may be None for descriptor-only data codecs
+
+            test_data = [b"test1", b"test2", b"test3"]
+            for i, data in enumerate(test_data):
+                packet = av.Packet(data)
+                packet.pts = i
+                packet.stream = data_stream
+                container.mux(packet)
+
+        with av.open(output_path) as newcontainer:
+            data_stream = newcontainer.streams.data[0]
+            klv_stream = newcontainer.streams.data[1]
+            assert data_stream.type == "data"
+            assert klv_stream.type == "data"
+            assert "bin_data" in str(data_stream)
+            assert "klv" in str(klv_stream)
+            assert data_stream.name == "bin_data"
+            assert klv_stream.name == "klv"
+        try:
+            os.remove(output_path)
+        except Exception:
+            pass
+
     def test_attachment_stream(self) -> None:
         input_path = av.datasets.curated(
             "pexels/time-lapse-video-of-night-sky-857195.mp4"