diff --git a/lib/compress/fse_compress.c b/lib/compress/fse_compress.c
index faca767c5..5547b4ac0 100644
--- a/lib/compress/fse_compress.c
+++ b/lib/compress/fse_compress.c
@@ -221,7 +221,11 @@ size_t FSE_buildCTable_wksp(FSE_CTable* ct,
 ****************************************************************/
 size_t FSE_NCountWriteBound(unsigned maxSymbolValue, unsigned tableLog)
 {
-    size_t const maxHeaderSize = (((maxSymbolValue+1) * tableLog) >> 3) + 3;
+    size_t const maxHeaderSize = (((maxSymbolValue+1) * tableLog
+                                   + 4 /* bitCount initialized at 4 */
+                                   + 2 /* first two symbols may use one additional bit each */) / 8)
+                                    + 1 /* round up to whole nb bytes */
+                                    + 2 /* additional two bytes for bitstream flush */;
     return maxSymbolValue ? maxHeaderSize : FSE_NCOUNTBOUND;  /* maxSymbolValue==0 ? use default */
 }
 
diff --git a/tests/fuzzer.c b/tests/fuzzer.c
index 9be7a38ab..696dd60c5 100644
--- a/tests/fuzzer.c
+++ b/tests/fuzzer.c
@@ -3357,6 +3357,23 @@ static int basicUnitTests(U32 const seed, double compressibility)
         FSE_normalizeCount(norm, tableLog, count, nbSeq, maxSymbolValue, /* useLowProbCount */ 1);
     }
     DISPLAYLEVEL(3, "OK \n");
+
+    DISPLAYLEVEL(3, "test%3i : testing FSE_writeNCount() PR#2779: ", testNb++);
+    {
+        size_t const outBufSize = 9;
+        short const count[11] = {1, 0, 1, 0, 1, 0, 1, 0, 1, 9, 18};
+        unsigned const tableLog = 5;
+        unsigned const maxSymbolValue = 10;
+        BYTE* outBuf = (BYTE*)malloc(outBufSize*sizeof(BYTE));
+
+        /* Ensure that this write doesn't write out of bounds, and that 
+         * FSE_writeNCount_generic() is *not* called with writeIsSafe == 1.
+         */
+        FSE_writeNCount(outBuf, outBufSize, count, maxSymbolValue, tableLog);
+        free(outBuf);
+    }
+    DISPLAYLEVEL(3, "OK \n");
+
 #ifdef ZSTD_MULTITHREAD
     DISPLAYLEVEL(3, "test%3i : passing wrong full dict should fail on compressStream2 refPrefix ", testNb++);
     {   ZSTD_CCtx* cctx = ZSTD_createCCtx();