diff --git a/mux/fmp4/src/fmp4mux/imp.rs b/mux/fmp4/src/fmp4mux/imp.rs
index c3886158..d6fede5d 100644
--- a/mux/fmp4/src/fmp4mux/imp.rs
+++ b/mux/fmp4/src/fmp4mux/imp.rs
@@ -984,27 +984,6 @@ impl FMP4Mux {
         // Check if this stream is filled enough now.
         if let Some(chunk_duration) = settings.chunk_duration {
             // In chunk mode
-            let (gop_idx, gop) = match stream
-                .queued_gops
-                .iter()
-                .enumerate()
-                .find(|(_idx, gop)| gop.final_earliest_pts || all_eos || stream.sinkpad.is_eos())
-            {
-                Some(res) => res,
-                None => {
-                    gst::trace!(CAT, obj: stream.sinkpad, "Chunked mode but no GOP with final earliest PTS known yet");
-                    return;
-                }
-            };
-
-            gst::trace!(
-                CAT,
-                obj: stream.sinkpad,
-                "GOP {gop_idx} start PTS {}, GOP end PTS {} (final {})",
-                gop.start_pts,
-                gop.end_pts,
-                gop.final_end_pts || all_eos || stream.sinkpad.is_eos(),
-            );
             gst::trace!(
                 CAT,
                 obj: stream.sinkpad,
@@ -1026,10 +1005,53 @@ impl FMP4Mux {
 
             // First check if the next split should be the end of a fragment or the end of a chunk.
             // If both are the same then a fragment split has preference.
-            if fragment_end_pts <= chunk_end_pts && gop.start_pts >= fragment_end_pts {
-                gst::debug!(CAT, obj: stream.sinkpad, "Stream queued enough data for finishing this fragment");
-                stream.fragment_filled = true;
-            } else if chunk_end_pts < fragment_end_pts {
+            if fragment_end_pts <= chunk_end_pts {
+                // We can only finish a fragment if a full GOP with final end PTS is queued and it
+                // ends at or after the fragment end PTS.
+                if let Some((gop_idx, gop)) = stream
+                    .queued_gops
+                    .iter()
+                    .enumerate()
+                    .find(|(_idx, gop)| gop.final_end_pts || all_eos || stream.sinkpad.is_eos())
+                {
+                    gst::trace!(
+                        CAT,
+                        obj: stream.sinkpad,
+                        "GOP {gop_idx} start PTS {}, GOP end PTS {}",
+                        gop.start_pts,
+                        gop.end_pts,
+                    );
+                    if gop.end_pts >= fragment_end_pts {
+                        gst::debug!(CAT, obj: stream.sinkpad, "Stream queued enough data for finishing this fragment");
+                        stream.fragment_filled = true;
+                        return;
+                    }
+                }
+            }
+
+            if !stream.fragment_filled {
+                let (gop_idx, gop) = match stream.queued_gops.iter().enumerate().find(
+                    |(_idx, gop)| gop.final_earliest_pts || all_eos || stream.sinkpad.is_eos(),
+                ) {
+                    Some(res) => res,
+                    None => {
+                        gst::trace!(
+                            CAT,
+                            obj: stream.sinkpad,
+                            "Chunked mode and want to finish fragment but no GOP with final end PTS known yet",
+                        );
+                        return;
+                    }
+                };
+
+                gst::trace!(
+                    CAT,
+                    obj: stream.sinkpad,
+                    "GOP {gop_idx} start PTS {}, GOP end PTS {} (final {})",
+                    gop.start_pts,
+                    gop.end_pts,
+                    gop.final_end_pts || all_eos || stream.sinkpad.is_eos(),
+                );
                 let last_pts = gop.buffers.last().map(|b| b.pts);
 
                 if gop.end_pts >= chunk_end_pts
@@ -1287,8 +1309,15 @@ impl FMP4Mux {
                         gop.final_end_pts || all_eos || stream.sinkpad.is_eos()
                     );
 
+                    // If we have a final GOP then include it as long as it's either
+                    //   - ending before the dequeue end PTS
+                    //   - no GOPs were dequeued yet and this is the first stream
+                    //
+                    // The second case would happen if no GOP ends between the last chunk of the
+                    // fragment and the fragment duration.
                     if (gop.final_end_pts || all_eos || stream.sinkpad.is_eos())
-                        && gop.end_pts <= dequeue_end_pts
+                        && (gop.end_pts <= dequeue_end_pts
+                            || (gops.is_empty() && chunk_end_pts.is_none()))
                     {
                         gst::trace!(
                             CAT,
@@ -1302,7 +1331,16 @@ impl FMP4Mux {
                         break;
                     }
 
-                    gst::error!(CAT, obj: stream.sinkpad, "Don't have a full GOP at the end of a fragment");
+                    // Otherwise if this is the first stream and no full GOP is queued then we need
+                    // to wait for more data.
+                    //
+                    // If this is not the first stream then take an incomplete GOP.
+                    if chunk_end_pts.is_none() {
+                        gst::info!(CAT, obj: stream.sinkpad, "Don't have a full GOP at the end of a fragment");
+                        return Err(gst_base::AGGREGATOR_FLOW_NEED_DATA);
+                    } else {
+                        gst::info!(CAT, obj: stream.sinkpad, "Including incomplete GOP");
+                    }
                 } else {
                     gst::trace!(
                         CAT,
@@ -1770,7 +1808,7 @@ impl FMP4Mux {
                         // This is handled below generally if nothing was dequeued
                     } else {
                         if settings.chunk_duration.is_some() {
-                            gst::warning!(
+                            gst::debug!(
                                 CAT,
                                 obj: stream.sinkpad,
                                 "Don't have anything to drain for the first stream on timeout in a live pipeline",
@@ -2144,6 +2182,19 @@ impl FMP4Mux {
         let min_earliest_pts = min_earliest_pts.unwrap();
         let chunk_end_pts = chunk_end_pts.unwrap();
 
+        gst::debug!(
+            CAT,
+            imp: self,
+            concat!(
+                "Draining chunk (fragment start: {} fragment end: {}) ",
+                "from PTS {} to {}"
+            ),
+            fragment_start,
+            fragment_filled,
+            min_earliest_pts,
+            chunk_end_pts,
+        );
+
         let mut fmp4_header = None;
         if !state.sent_headers {
             let mut buffer = state.stream_header.as_ref().unwrap().copy();
@@ -2315,11 +2366,7 @@ impl FMP4Mux {
                 Err(err) => {
                     if err == gst_base::AGGREGATOR_FLOW_NEED_DATA {
                         assert!(!all_eos);
-                        gst::element_imp_warning!(
-                            self,
-                            gst::StreamError::Format,
-                            ["Longer GOPs than fragment duration"]
-                        );
+                        gst::debug!(CAT, imp: self, "Need more data");
                         state.timeout_delay += 1.seconds();
                     }