diff --git a/libavformat/avformat.c b/libavformat/avformat.c
index 30d6ea6a49..1d0ac5ab7e 100644
--- a/libavformat/avformat.c
+++ b/libavformat/avformat.c
@@ -235,6 +235,47 @@ int ff_stream_side_data_copy(AVStream *dst, const AVStream *src)
     return 0;
 }
 
+int ff_stream_params_copy(AVStream *dst, const AVStream *src)
+{
+    int ret;
+
+    dst->id                  = src->id;
+    dst->time_base           = src->time_base;
+    dst->start_time          = src->start_time;
+    dst->duration            = src->duration;
+    dst->nb_frames           = src->nb_frames;
+    dst->disposition         = src->disposition;
+    dst->discard             = src->discard;
+    dst->sample_aspect_ratio = src->sample_aspect_ratio;
+    dst->avg_frame_rate      = src->avg_frame_rate;
+    dst->event_flags         = src->event_flags;
+    dst->r_frame_rate        = src->r_frame_rate;
+    dst->pts_wrap_bits       = src->pts_wrap_bits;
+
+    av_dict_free(&dst->metadata);
+    ret = av_dict_copy(&dst->metadata, src->metadata, 0);
+    if (ret < 0)
+        return ret;
+
+    ret = avcodec_parameters_copy(dst->codecpar, src->codecpar);
+    if (ret < 0)
+        return ret;
+
+    ret = ff_stream_side_data_copy(dst, src);
+    if (ret < 0)
+        return ret;
+
+    if (src->attached_pic.size > 0) {
+        ret = av_packet_ref(&dst->attached_pic, &src->attached_pic);
+        if (ret < 0)
+            return ret;
+    } else {
+        av_packet_unref(&dst->attached_pic);
+    }
+
+    return 0;
+}
+
 AVProgram *av_new_program(AVFormatContext *ac, int id)
 {
     AVProgram *program = NULL;
diff --git a/libavformat/fifo.c b/libavformat/fifo.c
index ead2bdc5cf..fef116d040 100644
--- a/libavformat/fifo.c
+++ b/libavformat/fifo.c
@@ -509,7 +509,7 @@ static int fifo_mux_init(AVFormatContext *avf, const AVOutputFormat *oformat,
         if (!st)
             return AVERROR(ENOMEM);
 
-        ret = ff_stream_encode_params_copy(st, avf->streams[i]);
+        ret = ff_stream_params_copy(st, avf->streams[i]);
         if (ret < 0)
             return ret;
     }
diff --git a/libavformat/internal.h b/libavformat/internal.h
index b6b8fbf56f..87a00bbae3 100644
--- a/libavformat/internal.h
+++ b/libavformat/internal.h
@@ -625,6 +625,18 @@ enum AVCodecID ff_get_pcm_codec_id(int bps, int flt, int be, int sflags);
  */
 int ff_stream_side_data_copy(AVStream *dst, const AVStream *src);
 
+/**
+ * Copy all stream parameters from source to destination stream, with the
+ * exception of:
+ *  * the index field, which is usually set by avformat_new_stream()
+ *  * the attached_pic field, if attached_pic.size is 0 or less
+ *
+ * @param dst pointer to destination AVStream
+ * @param src pointer to source AVStream
+ * @return >=0 on success, AVERROR code on error
+ */
+int ff_stream_params_copy(AVStream *dst, const AVStream *src);
+
 /**
  * Wrap ffurl_move() and log if error happens.
  *
diff --git a/libavformat/mux.h b/libavformat/mux.h
index c01da82194..1bfcaf795f 100644
--- a/libavformat/mux.h
+++ b/libavformat/mux.h
@@ -113,15 +113,6 @@ int ff_format_shift_data(AVFormatContext *s, int64_t read_start, int shift_size)
  */
 int ff_format_output_open(AVFormatContext *s, const char *url, AVDictionary **options);
 
-/**
- * Copy encoding parameters from source to destination stream
- *
- * @param dst pointer to destination AVStream
- * @param src pointer to source AVStream
- * @return >=0 on success, AVERROR code on error
- */
-int ff_stream_encode_params_copy(AVStream *dst, const AVStream *src);
-
 /**
  * Parse creation_time in AVFormatContext metadata if exists and warn if the
  * parsing fails.
diff --git a/libavformat/mux_utils.c b/libavformat/mux_utils.c
index eb8ea3d560..2fa2ab5b0f 100644
--- a/libavformat/mux_utils.c
+++ b/libavformat/mux_utils.c
@@ -121,34 +121,6 @@ int ff_format_output_open(AVFormatContext *s, const char *url, AVDictionary **op
     return 0;
 }
 
-int ff_stream_encode_params_copy(AVStream *dst, const AVStream *src)
-{
-    int ret;
-
-    dst->id                  = src->id;
-    dst->time_base           = src->time_base;
-    dst->nb_frames           = src->nb_frames;
-    dst->disposition         = src->disposition;
-    dst->sample_aspect_ratio = src->sample_aspect_ratio;
-    dst->avg_frame_rate      = src->avg_frame_rate;
-    dst->r_frame_rate        = src->r_frame_rate;
-
-    av_dict_free(&dst->metadata);
-    ret = av_dict_copy(&dst->metadata, src->metadata, 0);
-    if (ret < 0)
-        return ret;
-
-    ret = avcodec_parameters_copy(dst->codecpar, src->codecpar);
-    if (ret < 0)
-        return ret;
-
-    ret = ff_stream_side_data_copy(dst, src);
-    if (ret < 0)
-        return ret;
-
-    return 0;
-}
-
 int ff_parse_creation_time_metadata(AVFormatContext *s, int64_t *timestamp, int return_seconds)
 {
     AVDictionaryEntry *entry;
diff --git a/libavformat/segment.c b/libavformat/segment.c
index fa435d9f32..a8f3e94714 100644
--- a/libavformat/segment.c
+++ b/libavformat/segment.c
@@ -169,7 +169,7 @@ static int segment_mux_init(AVFormatContext *s)
 
         if (!(st = avformat_new_stream(oc, NULL)))
             return AVERROR(ENOMEM);
-        ret = ff_stream_encode_params_copy(st, ist);
+        ret = ff_stream_params_copy(st, ist);
         if (ret < 0)
             return ret;
         opar = st->codecpar;
diff --git a/libavformat/tee.c b/libavformat/tee.c
index f1f2a9d2a5..dbfad604d0 100644
--- a/libavformat/tee.c
+++ b/libavformat/tee.c
@@ -289,7 +289,7 @@ static int open_slave(AVFormatContext *avf, char *slave, TeeSlave *tee_slave)
             goto end;
         }
 
-        ret = ff_stream_encode_params_copy(st2, st);
+        ret = ff_stream_params_copy(st2, st);
         if (ret < 0)
             goto end;
     }
diff --git a/libavformat/webm_chunk.c b/libavformat/webm_chunk.c
index d69db3a004..39f21fce7a 100644
--- a/libavformat/webm_chunk.c
+++ b/libavformat/webm_chunk.c
@@ -94,7 +94,7 @@ static int webm_chunk_init(AVFormatContext *s)
     if (!(st = avformat_new_stream(oc, NULL)))
         return AVERROR(ENOMEM);
 
-    if ((ret = ff_stream_encode_params_copy(st, ost)) < 0)
+    if ((ret = ff_stream_params_copy(st, ost)) < 0)
         return ret;
 
     if (wc->http_method)
