diff --git a/py/mpz.h b/py/mpz.h
index b00d2b6555..e287cdd105 100644
--- a/py/mpz.h
+++ b/py/mpz.h
@@ -78,8 +78,9 @@ typedef int8_t mpz_dbl_dig_signed_t;
   #define MPZ_LONG_1 1L
 #endif
 
-#define MPZ_NUM_DIG_FOR_INT (sizeof(mp_int_t) * 8 / MPZ_DIG_SIZE + 1)
-#define MPZ_NUM_DIG_FOR_LL (sizeof(long long) * 8 / MPZ_DIG_SIZE + 1)
+// these define the maximum storage needed to hold an int or long long
+#define MPZ_NUM_DIG_FOR_INT ((sizeof(mp_int_t) * 8 + MPZ_DIG_SIZE - 1) / MPZ_DIG_SIZE)
+#define MPZ_NUM_DIG_FOR_LL ((sizeof(long long) * 8 + MPZ_DIG_SIZE - 1) / MPZ_DIG_SIZE)
 
 typedef struct _mpz_t {
     mp_uint_t neg : 1;
diff --git a/py/objint_mpz.c b/py/objint_mpz.c
index 27f1ddbfc8..69a81d2c39 100644
--- a/py/objint_mpz.c
+++ b/py/objint_mpz.c
@@ -44,23 +44,34 @@
 #if MICROPY_PY_SYS_MAXSIZE
 // Export value for sys.maxsize
 #define DIG_MASK ((MPZ_LONG_1 << MPZ_DIG_SIZE) - 1)
-STATIC const mpz_dig_t maxsize_dig[MPZ_NUM_DIG_FOR_INT] = {
+STATIC const mpz_dig_t maxsize_dig[] = {
+    #define NUM_DIG 1
     (MP_SSIZE_MAX >> MPZ_DIG_SIZE * 0) & DIG_MASK,
     #if (MP_SSIZE_MAX >> MPZ_DIG_SIZE * 0) > DIG_MASK
-    (MP_SSIZE_MAX >> MPZ_DIG_SIZE * 1) & DIG_MASK,
-    #if (MP_SSIZE_MAX >> MPZ_DIG_SIZE * 1) > DIG_MASK
-    (MP_SSIZE_MAX >> MPZ_DIG_SIZE * 2) & DIG_MASK,
-    (MP_SSIZE_MAX >> MPZ_DIG_SIZE * 3) & DIG_MASK,
-    (MP_SSIZE_MAX >> MPZ_DIG_SIZE * 4) & DIG_MASK,
-//    (MP_SSIZE_MAX >> MPZ_DIG_SIZE * 5) & DIG_MASK,
-    #endif
+     #undef NUM_DIG
+     #define NUM_DIG 2
+     (MP_SSIZE_MAX >> MPZ_DIG_SIZE * 1) & DIG_MASK,
+     #if (MP_SSIZE_MAX >> MPZ_DIG_SIZE * 1) > DIG_MASK
+      #undef NUM_DIG
+      #define NUM_DIG 3
+      (MP_SSIZE_MAX >> MPZ_DIG_SIZE * 2) & DIG_MASK,
+      #if (MP_SSIZE_MAX >> MPZ_DIG_SIZE * 2) > DIG_MASK
+       #undef NUM_DIG
+       #define NUM_DIG 4
+       (MP_SSIZE_MAX >> MPZ_DIG_SIZE * 3) & DIG_MASK,
+       #if (MP_SSIZE_MAX >> MPZ_DIG_SIZE * 3) > DIG_MASK
+        #error cannot encode MP_SSIZE_MAX as mpz
+       #endif
+      #endif
+     #endif
     #endif
 };
 const mp_obj_int_t mp_maxsize_obj = {
     {&mp_type_int},
-    {.fixed_dig = 1, .len = MPZ_NUM_DIG_FOR_INT, .alloc = MPZ_NUM_DIG_FOR_INT, .dig = (mpz_dig_t*)maxsize_dig}
+    {.fixed_dig = 1, .len = NUM_DIG, .alloc = NUM_DIG, .dig = (mpz_dig_t*)maxsize_dig}
 };
 #undef DIG_MASK
+#undef NUM_DIG
 #endif
 
 STATIC mp_obj_int_t *mp_obj_int_new_mpz(void) {
diff --git a/tests/basics/int_mpz.py b/tests/basics/int_mpz.py
index 6d99accf27..8c347302a5 100644
--- a/tests/basics/int_mpz.py
+++ b/tests/basics/int_mpz.py
@@ -77,3 +77,7 @@ x = 4611686018427387903 # small
 x = -4611686018427387903 # small
 x = 4611686018427387904 # big
 x = -4611686018427387904 # big
+
+# sys.maxsize is a constant mpz, so test it's compatible with dynamic ones
+import sys
+print(sys.maxsize + 1 - 1 == sys.maxsize)