diff --git a/libavformat/mux.c b/libavformat/mux.c
index 2241dbe0e6..1c15a91cd0 100644
--- a/libavformat/mux.c
+++ b/libavformat/mux.c
@@ -538,7 +538,7 @@ static int write_packet(AVFormatContext *s, AVPacket *pkt)
         AVStream *st = s->streams[pkt->stream_index];
         int64_t offset = st->mux_ts_offset;
 
-        if (pkt->dts < 0 && pkt->dts != AV_NOPTS_VALUE && !s->offset) {
+        if ((pkt->dts < 0 || s->avoid_negative_ts == 2) && pkt->dts != AV_NOPTS_VALUE && !s->offset) {
             s->offset = -pkt->dts;
             s->offset_timebase = st->time_base;
         }
diff --git a/libavformat/options_table.h b/libavformat/options_table.h
index ca30fd29e3..2e08682f43 100644
--- a/libavformat/options_table.h
+++ b/libavformat/options_table.h
@@ -73,7 +73,7 @@ static const AVOption avformat_options[] = {
 {"compliant",  "consider all spec non compliancies as errors", 0, AV_OPT_TYPE_CONST, {.i64 = AV_EF_COMPLIANT }, INT_MIN, INT_MAX, D, "err_detect"},
 {"aggressive", "consider things that a sane encoder shouldn't do as an error", 0, AV_OPT_TYPE_CONST, {.i64 = AV_EF_AGGRESSIVE }, INT_MIN, INT_MAX, D, "err_detect"},
 {"use_wallclock_as_timestamps", "use wallclock as timestamps", OFFSET(use_wallclock_as_timestamps), AV_OPT_TYPE_INT, {.i64 = 0}, 0, INT_MAX-1, D},
-{"avoid_negative_ts", "shift timestamps to make them non-negative. 1 enables, 0 disables, default of -1 enables when required by target format.", OFFSET(avoid_negative_ts), AV_OPT_TYPE_INT, {.i64 = -1}, -1, 1, E},
+{"avoid_negative_ts", "shift timestamps so they start at 0. 1 enable if negative ts, 2 enable, 0 disables, default of -1 enables when required by target format.", OFFSET(avoid_negative_ts), AV_OPT_TYPE_INT, {.i64 = -1}, -1, 2, E},
 {"skip_initial_bytes", "set number of bytes to skip before reading header and frames", OFFSET(skip_initial_bytes), AV_OPT_TYPE_INT, {.i64 = 0}, 0, INT_MAX-1, D},
 {"correct_ts_overflow", "correct single timestamp overflows", OFFSET(correct_ts_overflow), AV_OPT_TYPE_INT, {.i64 = 1}, 0, 1, D},
 {"flush_packets", "enable flushing of the I/O context after each packet", OFFSET(flush_packets), AV_OPT_TYPE_INT, {.i64 = 1}, 0, 1, E},