diff --git a/lib/compress/zstd_opt.c b/lib/compress/zstd_opt.c
index 97902cd9..dcca6ed5 100644
--- a/lib/compress/zstd_opt.c
+++ b/lib/compress/zstd_opt.c
@@ -1086,8 +1086,7 @@ static void ZSTD_initStats_ultra(
     assert(ms->opt.litLengthSum == 0);    /* first block */
     assert(seqStore->sequences == seqStore->sequencesStart);   /* no ldm */
     assert(ms->window.dictLimit == ms->window.lowLimit);   /* no dictionary */
-    assert(ms->nextToUpdate >= ms->window.dictLimit
-        && ms->nextToUpdate <= ms->window.dictLimit + 1);
+    assert(ms->window.dictLimit - ms->nextToUpdate <= 1);  /* no prefix (note: intentional overflow, defined as 2-complement) */
 
     memcpy(tmpRep, rep, sizeof(tmpRep));
     ZSTD_compressBlock_opt_generic(ms, seqStore, tmpRep, src, srcSize, 2 /*optLevel*/, ZSTD_noDict);   /* generate stats into ms->opt*/
@@ -1121,12 +1120,17 @@ size_t ZSTD_compressBlock_btultra2(
     /* 2-pass strategy
      * this strategy makes a first pass over first block to collect statistics
      * and seed next round's statistics with it.
+     * After 1st pass, function forgets everything, and starts a new block.
+     * Consequently, this can only work if no data has been previously loaded in tables,
+     * aka, no dictionary, no prefix, no ldm preprocessing.
      * The compression ratio gain is generally small (~0.5% on first block),
      * the cost is 2x cpu time on first block. */
     assert(srcSize <= ZSTD_BLOCKSIZE_MAX);
     if ( (ms->opt.litLengthSum==0)   /* first block */
-      && (seqStore->sequences == seqStore->sequencesStart)   /* no ldm */
-      && (ms->window.dictLimit == ms->window.lowLimit) ) {   /* no dictionary */
+      && (seqStore->sequences == seqStore->sequencesStart)  /* no ldm */
+      && (ms->window.dictLimit == ms->window.lowLimit)   /* no dictionary */
+      && (ms->window.dictLimit - ms->nextToUpdate <= 1)  /* no prefix (note: intentional overflow, defined as 2-complement) */
+      ) {
         ZSTD_initStats_ultra(ms, seqStore, rep, src, srcSize);
     }
 
diff --git a/tests/zstreamtest.c b/tests/zstreamtest.c
index 4ff1d353..0de58b66 100644
--- a/tests/zstreamtest.c
+++ b/tests/zstreamtest.c
@@ -1548,7 +1548,7 @@ static int fuzzerTests_MT(U32 seed, U32 nbTests, unsigned startTest,
                     params.fParams.contentSizeFlag = FUZ_rand(&lseed) & 1;
                     DISPLAYLEVEL(5, "checksumFlag : %u \n", params.fParams.checksumFlag);
                     CHECK_Z( ZSTDMT_setMTCtxParameter(zc, ZSTDMT_p_overlapSectionLog, FUZ_rand(&lseed) % 12) );
-                    CHECK_Z( ZSTDMT_setMTCtxParameter(zc, ZSTDMT_p_jobSize, FUZ_rand(&lseed) % (2*maxTestSize+1)) );   /* custome job size */
+                    CHECK_Z( ZSTDMT_setMTCtxParameter(zc, ZSTDMT_p_jobSize, FUZ_rand(&lseed) % (2*maxTestSize+1)) );   /* custom job size */
                     CHECK_Z( ZSTDMT_initCStream_advanced(zc, dict, dictSize, params, pledgedSrcSize) );
         }   }   }