diff --git a/libavcodec/pngenc.c b/libavcodec/pngenc.c
index 2393161c3b..81b95c143d 100644
--- a/libavcodec/pngenc.c
+++ b/libavcodec/pngenc.c
@@ -412,14 +412,25 @@ static int encode_headers(AVCodecContext *avctx, const AVFrame *pict)
         }
     }
 
+    side_data = av_frame_get_side_data(pict, AV_FRAME_DATA_ICC_PROFILE);
+    if ((ret = png_write_iccp(s, side_data)))
+        return ret;
+
     /* write colorspace information */
     if (pict->color_primaries == AVCOL_PRI_BT709 &&
         pict->color_trc == AVCOL_TRC_IEC61966_2_1) {
         s->buf[0] = 1; /* rendering intent, relative colorimetric by default */
         png_write_chunk(&s->bytestream, MKTAG('s', 'R', 'G', 'B'), s->buf, 1);
-    } else if (pict->color_primaries != AVCOL_PRI_UNSPECIFIED ||
-        pict->color_trc != AVCOL_TRC_UNSPECIFIED) {
-        /* these values match H.273 so no translation is needed */
+    } else if (pict->color_trc != AVCOL_TRC_UNSPECIFIED && !side_data) {
+        /*
+         * Avoid writing cICP if the transfer is unknown. Known primaries
+         * with unknown transfer can be handled by cHRM.
+         *
+         * We also avoid writing cICP if an ICC Profile is present, because
+         * the standard requires that cICP overrides iCCP.
+         *
+         * These values match H.273 so no translation is needed.
+         */
         s->buf[0] = pict->color_primaries;
         s->buf[1] = pict->color_trc;
         s->buf[2] = 0; /* colorspace = RGB */
@@ -432,10 +443,6 @@ static int encode_headers(AVCodecContext *avctx, const AVFrame *pict)
     if (png_get_gama(pict->color_trc, s->buf))
         png_write_chunk(&s->bytestream, MKTAG('g', 'A', 'M', 'A'), s->buf, 4);
 
-    side_data = av_frame_get_side_data(pict, AV_FRAME_DATA_ICC_PROFILE);
-    if ((ret = png_write_iccp(s, side_data)))
-        return ret;
-
     /* put the palette if needed, must be after colorspace information */
     if (s->color_type == PNG_COLOR_TYPE_PALETTE) {
         int has_alpha, alpha, i;