diff --git a/lib/compress/fse_compress.c b/lib/compress/fse_compress.c
index 07b3ab89b..70daae3bc 100644
--- a/lib/compress/fse_compress.c
+++ b/lib/compress/fse_compress.c
@@ -331,7 +331,7 @@ void FSE_freeCTable (FSE_CTable* ct) { free(ct); }
 /* provides the minimum logSize to safely represent a distribution */
 static unsigned FSE_minTableLog(size_t srcSize, unsigned maxSymbolValue)
 {
-    U32 minBitsSrc = BIT_highbit32((U32)(srcSize - 1)) + 1;
+    U32 minBitsSrc = BIT_highbit32((U32)(srcSize)) + 1;
     U32 minBitsSymbols = BIT_highbit32(maxSymbolValue) + 2;
     U32 minBits = minBitsSrc < minBitsSymbols ? minBitsSrc : minBitsSymbols;
     assert(srcSize > 1); /* Not supported, RLE should be used instead */
@@ -394,6 +394,9 @@ static size_t FSE_normalizeM2(short* norm, U32 tableLog, const unsigned* count,
     }
     ToDistribute = (1 << tableLog) - distributed;
 
+    if (ToDistribute == 0)
+        return 0;
+
     if ((total / ToDistribute) > lowOne) {
         /* risk of rounding to zero */
         lowOne = (U32)((total * 3) / (ToDistribute * 2));
diff --git a/tests/fuzzer.c b/tests/fuzzer.c
index f7bacd5ca..8856a504a 100644
--- a/tests/fuzzer.c
+++ b/tests/fuzzer.c
@@ -27,6 +27,7 @@
 #include <string.h>       /* strcmp */
 #include <assert.h>
 #define ZSTD_STATIC_LINKING_ONLY  /* ZSTD_compressContinue, ZSTD_compressBlock */
+#include "fse.h"
 #include "zstd.h"         /* ZSTD_VERSION_STRING */
 #include "zstd_errors.h"  /* ZSTD_getErrorCode */
 #include "zstdmt_compress.h"
@@ -1423,6 +1424,24 @@ static int basicUnitTests(U32 seed, double compressibility)
     }
     DISPLAYLEVEL(3, "OK \n");
 
+    DISPLAYLEVEL(3, "test%3i : testing FSE_normalizeCount() PR#1255: ", testNb++);
+    {
+        short norm[32];
+        unsigned count[32];
+        unsigned const tableLog = 5;
+        size_t const nbSeq = 32;
+        unsigned const maxSymbolValue = 31;
+        size_t i;
+
+        for (i = 0; i < 32; ++i)
+            count[i] = 1;
+        /* Calling FSE_normalizeCount() on a uniform distribution should not
+         * cause a division by zero.
+         */
+        FSE_normalizeCount(norm, tableLog, count, nbSeq, maxSymbolValue);
+    }
+    DISPLAYLEVEL(3, "OK \n");
+
 _end:
     free(CNBuffer);
     free(compressedBuffer);