diff --git a/libavcodec/speedhq.c b/libavcodec/speedhq.c
index 4f6a539ad8..91ba80ebd3 100644
--- a/libavcodec/speedhq.c
+++ b/libavcodec/speedhq.c
@@ -155,8 +155,6 @@ static const uint8_t unscaled_quant_matrix[64] = {
     27, 29, 35, 38, 46, 56, 69, 83
 };
 
-static uint8_t speedhq_static_rl_table_store[2][2*MAX_RUN + MAX_LEVEL + 3];
-
 static VLC dc_lum_vlc_le;
 static VLC dc_chroma_vlc_le;
 static VLC dc_alpha_run_vlc_le;
@@ -648,7 +646,6 @@ static av_cold void speedhq_static_init(void)
                            ff_mpeg12_vlc_dc_chroma_code, 2, 2,
                            INIT_VLC_OUTPUT_LE, 514);
 
-    ff_rl_init(&ff_rl_speedhq, speedhq_static_rl_table_store);
     INIT_2D_VLC_RL(ff_rl_speedhq, 674, INIT_VLC_LE);
 
     compute_alpha_vlcs();
@@ -733,5 +730,6 @@ const AVCodec ff_speedhq_decoder = {
     .init           = speedhq_decode_init,
     .decode         = speedhq_decode_frame,
     .capabilities   = AV_CODEC_CAP_DR1,
+    .caps_internal  = FF_CODEC_CAP_INIT_THREADSAFE,
 };
 #endif /* CONFIG_SPEEDHQ_DECODER */
diff --git a/libavcodec/speedhqenc.c b/libavcodec/speedhqenc.c
index 6ff7b447a0..529df4f5b6 100644
--- a/libavcodec/speedhqenc.c
+++ b/libavcodec/speedhqenc.c
@@ -298,7 +298,7 @@ const AVCodec ff_speedhq_encoder = {
     .init           = ff_mpv_encode_init,
     .encode2        = ff_mpv_encode_picture,
     .close          = ff_mpv_encode_end,
-    .caps_internal  = FF_CODEC_CAP_INIT_CLEANUP,
+    .caps_internal  = FF_CODEC_CAP_INIT_THREADSAFE | FF_CODEC_CAP_INIT_CLEANUP,
     .pix_fmts       = (const enum AVPixelFormat[]) {
         AV_PIX_FMT_YUV420P, AV_PIX_FMT_YUV422P, AV_PIX_FMT_YUV444P,
         AV_PIX_FMT_NONE