diff --git a/libavcodec/mpeg4videoenc.h b/libavcodec/mpeg4videoenc.h
index 815f16f073..4e20b8aaa0 100644
--- a/libavcodec/mpeg4videoenc.h
+++ b/libavcodec/mpeg4videoenc.h
@@ -27,6 +27,18 @@
 
 #include "put_bits.h"
 
+enum {
+    MAX_PB2_INTRA_SIZE = 1 /* ac_pred */ + 5 /* max cbpy len */ +
+                         2 /* dquant */ + 1 /* interlaced dct */
+                         + 4 * (8 /* longest luma dct_dc_size */ +
+                                9 /* longest dc diff */ + 1 /* marker */)
+                         + 2 * (9 + 9 + 1),
+    MAX_PB2_INTER_SIZE = 5 /* max cbpy len */ +
+                         2 /* dquant */ + 1 /* interlaced_dct */ + 1,
+    MAX_PB2_MB_SIZE    = (FFMAX(MAX_PB2_INTER_SIZE, MAX_PB2_INTRA_SIZE) + 7) / 8,
+    MAX_AC_TEX_MB_SIZE = 64 * 6 * 30 /* longest escape code */ / 8,
+};
+
 typedef struct MPVEncContext MPVEncContext;
 
 void ff_set_mpeg4_time(MPVEncContext *s);
diff --git a/libavcodec/mpegvideo_enc.c b/libavcodec/mpegvideo_enc.c
index 948022c1c2..313c2e5744 100644
--- a/libavcodec/mpegvideo_enc.c
+++ b/libavcodec/mpegvideo_enc.c
@@ -2979,14 +2979,15 @@ static int encode_thread(AVCodecContext *c, void *arg){
     int i;
     MBBackup best_s = { 0 }, backup_s;
     uint8_t bit_buf[2][MAX_MB_BYTES];
-    uint8_t bit_buf2[2][MAX_MB_BYTES];
-    uint8_t bit_buf_tex[2][MAX_MB_BYTES];
+    // + 2 because ff_copy_bits() overreads
+    uint8_t bit_buf2[2][MAX_PB2_MB_SIZE + 2];
+    uint8_t bit_buf_tex[2][MAX_AC_TEX_MB_SIZE + 2];
     PutBitContext pb[2], pb2[2], tex_pb[2];
 
     for(i=0; i<2; i++){
         init_put_bits(&pb    [i], bit_buf    [i], MAX_MB_BYTES);
-        init_put_bits(&pb2   [i], bit_buf2   [i], MAX_MB_BYTES);
-        init_put_bits(&tex_pb[i], bit_buf_tex[i], MAX_MB_BYTES);
+        init_put_bits(&pb2   [i], bit_buf2   [i], MAX_PB2_MB_SIZE);
+        init_put_bits(&tex_pb[i], bit_buf_tex[i], MAX_AC_TEX_MB_SIZE);
     }
 
     s->last_bits= put_bits_count(&s->pb);