diff --git a/startup.4th b/startup.4th
index 86fe31a..5062ae5 100644
--- a/startup.4th
+++ b/startup.4th
@@ -1366,6 +1366,7 @@ VARIABLE TOTAL
 >>FORTH
 
 : ALLOCATE ( size -- obj-addr )
+   DUP 0= IF EXIT THEN
    CELL+ DUP BUDDY-MAX-BYTES U> IF
       PAGESIZE ALIGNED-TO DUP MMAP-ALLOCATE TUCK ! CELL+ EXIT
    THEN
@@ -1378,12 +1379,14 @@ VARIABLE TOTAL
    SWAP OVER ! CELL+ ;
 
 : FREE ( obj-addr -- )
-   CELL- DUP @
-   DUP BUDDY-ORDERS U< IF SWAP BUDDY-FREE EXIT THEN
-   BEGIN
-      2DUP SYS_MUNMAP SYSCALL2 ?DUP 0= IF 2DROP EXIT THEN
-      NEGATE ERRNO_EINTR <> "munmap failed" ?FAIL
-   AGAIN ;
+   ?DUP IF
+      CELL- DUP @
+      DUP BUDDY-ORDERS U< IF SWAP BUDDY-FREE EXIT THEN
+      BEGIN
+         2DUP SYS_MUNMAP SYSCALL2 ?DUP 0= IF 2DROP EXIT THEN
+         NEGATE ERRNO_EINTR <> "munmap failed" ?FAIL
+      AGAIN
+   THEN ;
 
 >>SYSTEM
 
@@ -1392,7 +1395,16 @@ VARIABLE TOTAL
 
 >>FORTH
 
-: RESIZE ( obj-addr1 size -- obj-addr1 | obj-addr2 )
+\ If size is 0 then free obj-addr1 (which may be zero / NULL) and return 0
+\ Otherwise if obj-addr1 is 0 (NULL) then allocate size bytes
+\ If neither obj-addr1 nor size is 0 then return an object with allocated size
+\ greater than or equal to size containing the same bytes as obj-addr1 up to
+\ size or the original object size, whichever is less
+\ The returned address may be equal to obj-addr1; if it is not, the original
+\ obj-addr1 is freed and no longer valid
+: RESIZE ( obj-addr1 size -- obj-addr1 | obj-addr2 | 0 )
+   DUP 0= IF DROP FREE 0 EXIT THEN
+   OVER 0= IF NIP ALLOCATE EXIT THEN
    OVER OBJECT-SIZE CELL+ OVER CELL+ BUDDY-MIN-BYTES UMAX 2DUP U>= IF
       \ Allocated space is larger than requested size, shrink if <= 50% used
       ( S: obj-addr1 size obj-size req-size )
diff --git a/test/allocate.4th b/test/allocate.4th
index 8407800..cb1a370 100644
--- a/test/allocate.4th
+++ b/test/allocate.4th
@@ -24,6 +24,12 @@
       ?DUP
    WHILE
       DUP @ SWAP FREE
-   REPEAT ;
+   REPEAT
+
+   "Allocate 0 bytes" HEADING
+   0 ALLOCATE "Result: " TYPE U. EOL
+
+   "Free a NULL pointer" HEADING
+   0 FREE ;
 
 TEST
diff --git a/test/allocate.exp b/test/allocate.exp
index 34b3f4f..0508090 100644
--- a/test/allocate.exp
+++ b/test/allocate.exp
@@ -2,4 +2,7 @@
 * Free large object
 * Allocate 1000 small objects (200 B)
 * Free 1000 small objects
+* Allocate 0 bytes
+Result: 0
+* Free a NULL pointer
 exit-code: 0