diff --git a/ldump.c b/ldump.c
index 34cfb576..0d20fb0a 100644
--- a/ldump.c
+++ b/ldump.c
@@ -30,7 +30,7 @@ typedef struct {
   int strip;
   int status;
   Table *h;  /* table to track saved strings */
-  lua_Unsigned nstr;  /* counter to number saved strings */
+  lua_Integer nstr;  /* counter for counting saved strings */
 } DumpState;
 
 
@@ -86,12 +86,12 @@ static void dumpByte (DumpState *D, int y) {
 ** size for 'dumpVarint' buffer: each byte can store up to 7 bits.
 ** (The "+6" rounds up the division.)
 */
-#define DIBS    ((sizeof(varint_t) * CHAR_BIT + 6) / 7)
+#define DIBS    ((sizeof(size_t) * CHAR_BIT + 6) / 7)
 
 /*
 ** Dumps an unsigned integer using the MSB Varint encoding
 */
-static void dumpVarint (DumpState *D, varint_t x) {
+static void dumpVarint (DumpState *D, size_t x) {
   lu_byte buff[DIBS];
   int n = 1;
   buff[DIBS - 1] = x & 0x7f;  /* fill least-significant byte */
@@ -101,9 +101,13 @@ static void dumpVarint (DumpState *D, varint_t x) {
 }
 
 
+static void dumpSize (DumpState *D, size_t sz) {
+  dumpVarint(D, sz);
+}
+
 static void dumpInt (DumpState *D, int x) {
   lua_assert(x >= 0);
-  dumpVarint(D, x);
+  dumpVarint(D, cast(size_t, x));
 }
 
 
@@ -126,22 +130,22 @@ static void dumpInteger (DumpState *D, lua_Integer x) {
 */
 static void dumpString (DumpState *D, TString *ts) {
   if (ts == NULL)
-    dumpVarint(D, 0);
+    dumpSize(D, 0);
   else {
     TValue idx;
     if (luaH_getstr(D->h, ts, &idx) == HOK) {  /* string already saved? */
-      dumpVarint(D, 1);  /* reuse a saved string */
-      dumpVarint(D, l_castS2U(ivalue(&idx)));  /* index of saved string */
+      dumpSize(D, 1);  /* reuse a saved string */
+      dumpSize(D, cast_sizet(ivalue(&idx)));  /* index of saved string */
     }
     else {  /* must write and save the string */
       TValue key, value;  /* to save the string in the hash */
       size_t size;
       const char *s = getlstr(ts, size);
-      dumpVarint(D, size + 2);
+      dumpSize(D, size + 2);
       dumpVector(D, s, size + 1);  /* include ending '\0' */
       D->nstr++;  /* one more saved string */
       setsvalue(D->L, &key, ts);  /* the string is the key */
-      setivalue(&value, l_castU2S(D->nstr));  /* its index is the value */
+      setivalue(&value, D->nstr);  /* its index is the value */
       luaH_set(D->L, D->h, &key, &value);  /* h[ts] = nstr */
       /* integer value does not need barrier */
     }
diff --git a/lundump.c b/lundump.c
index d485f266..51d5dc66 100644
--- a/lundump.c
+++ b/lundump.c
@@ -36,8 +36,8 @@ typedef struct {
   ZIO *Z;
   const char *name;
   Table *h;  /* list for string reuse */
-  size_t offset;  /* current position relative to beginning of dump */
-  lua_Unsigned nstr;  /* number of strings in the list */
+  lu_mem offset;  /* current position relative to beginning of dump */
+  lua_Integer nstr;  /* number of strings in the list */
   lu_byte fixed;  /* dump is fixed in memory */
 } LoadState;
 
@@ -94,13 +94,13 @@ static lu_byte loadByte (LoadState *S) {
 }
 
 
-static varint_t loadVarint (LoadState *S, varint_t limit) {
-  varint_t x = 0;
+static size_t loadVarint (LoadState *S, size_t limit) {
+  size_t x = 0;
   int b;
   limit >>= 7;
   do {
     b = loadByte(S);
-    if (x >= limit)
+    if (x > limit)
       error(S, "integer overflow");
     x = (x << 7) | (b & 0x7f);
   } while ((b & 0x80) != 0);
@@ -109,12 +109,12 @@ static varint_t loadVarint (LoadState *S, varint_t limit) {
 
 
 static size_t loadSize (LoadState *S) {
-  return cast_sizet(loadVarint(S, MAX_SIZET));
+  return loadVarint(S, MAX_SIZET);
 }
 
 
 static int loadInt (LoadState *S) {
-  return cast_int(loadVarint(S, INT_MAX));
+  return cast_int(loadVarint(S, cast_sizet(INT_MAX)));
 }
 
 
@@ -148,10 +148,9 @@ static void loadString (LoadState *S, Proto *p, TString **sl) {
     return;
   }
   else if (size == 1) {  /* previously saved string? */
-    /* get its index */
-    lua_Unsigned idx = cast(lua_Unsigned, loadVarint(S, LUA_MAXUNSIGNED));
+    lua_Integer idx = cast(lua_Integer, loadSize(S));  /* get its index */
     TValue stv;
-    luaH_getint(S->h, l_castU2S(idx), &stv);  /* get its value */
+    luaH_getint(S->h, idx, &stv);  /* get its value */
     *sl = ts = tsvalue(&stv);
     luaC_objbarrier(L, p, ts);
     return;  /* do not save it again */
@@ -175,7 +174,7 @@ static void loadString (LoadState *S, Proto *p, TString **sl) {
   /* add string to list of saved strings */
   S->nstr++;
   setsvalue(L, &sv, ts);
-  luaH_setint(L, S->h, l_castU2S(S->nstr), &sv);
+  luaH_setint(L, S->h, S->nstr, &sv);
   luaC_objbarrierback(L, obj2gco(S->h), ts);
 }
 
diff --git a/lundump.h b/lundump.h
index ff66d2e7..1d6e50ea 100644
--- a/lundump.h
+++ b/lundump.h
@@ -28,18 +28,6 @@
 #define LUAC_FORMAT	0	/* this is the official format */
 
 
-/*
-** Type to handle MSB Varint encoding: Try to get the largest unsigned
-** integer available. (It was enough to be the largest between size_t and
-** lua_Integer, but the C89 preprocessor knows nothing about size_t.)
-*/
-#if !defined(LUA_USE_C89) && defined(LLONG_MAX)
-typedef unsigned long long varint_t;
-#else
-typedef unsigned long varint_t;
-#endif
-
-
 /* load one chunk; from lundump.c */
 LUAI_FUNC LClosure* luaU_undump (lua_State* L, ZIO* Z, const char* name,
                                                int fixed);