diff --git a/changes/laplace-edge-cases b/changes/laplace-edge-cases
index f8a36e1de3..266b119bd9 100644
--- a/changes/laplace-edge-cases
+++ b/changes/laplace-edge-cases
@@ -3,5 +3,9 @@
        * avoid division by zero
        * avoid taking the log of zero
        * silence clang type conversion warnings using round and trunc
-    - Add tests for laplace edge cases.
+       * consistently check for overflow in round_*_to_next_multiple_of
+    - Add tests for laplace edge cases:
+       * check add_laplace_noise with maximal values
+       * check round_*_to_next_multiple_of with additional values
+       * check round_*_to_next_multiple_of with maximal values
       Related to HS stats in #13192.
diff --git a/src/common/util.c b/src/common/util.c
index 52b3e04946..3e680d2d9e 100644
--- a/src/common/util.c
+++ b/src/common/util.c
@@ -491,7 +491,9 @@ round_to_power_of_2(uint64_t u64)
 unsigned
 round_to_next_multiple_of(unsigned number, unsigned divisor)
 {
-  number += divisor - 1;
+  tor_assert(divisor > 0);
+  if (UINT_MAX - divisor + 1 >= number)
+    number += divisor - 1;
   number -= number % divisor;
   return number;
 }
@@ -501,7 +503,9 @@ round_to_next_multiple_of(unsigned number, unsigned divisor)
 uint32_t
 round_uint32_to_next_multiple_of(uint32_t number, uint32_t divisor)
 {
-  number += divisor - 1;
+  tor_assert(divisor > 0);
+  if (UINT32_MAX - divisor + 1 >= number)
+    number += divisor - 1;
   number -= number % divisor;
   return number;
 }
@@ -511,7 +515,9 @@ round_uint32_to_next_multiple_of(uint32_t number, uint32_t divisor)
 uint64_t
 round_uint64_to_next_multiple_of(uint64_t number, uint64_t divisor)
 {
-  number += divisor - 1;
+  tor_assert(divisor > 0);
+  if (UINT64_MAX - divisor + 1 >= number)
+    number += divisor - 1;
   number -= number % divisor;
   return number;
 }
diff --git a/src/test/test_util.c b/src/test/test_util.c
index 940f9bde52..74d7227191 100644
--- a/src/test/test_util.c
+++ b/src/test/test_util.c
@@ -4054,8 +4054,11 @@ test_util_round_to_next_multiple_of(void *arg)
   tt_u64_op(round_uint64_to_next_multiple_of(99,7), ==, 105);
   tt_u64_op(round_uint64_to_next_multiple_of(99,9), ==, 99);
 
-  tt_i64_op(round_int64_to_next_multiple_of(0,1), ==, 0);
-  tt_i64_op(round_int64_to_next_multiple_of(0,7), ==, 0);
+  tt_assert(round_uint64_to_next_multiple_of(UINT64_MAX,2) ==
+            UINT64_MAX-UINT64_MAX%2);
+
+  tt_assert(round_int64_to_next_multiple_of(0,1) == 0);
+  tt_assert(round_int64_to_next_multiple_of(0,7) == 0);
 
   tt_i64_op(round_int64_to_next_multiple_of(99,1), ==, 99);
   tt_i64_op(round_int64_to_next_multiple_of(99,7), ==, 105);
@@ -4068,6 +4071,26 @@ test_util_round_to_next_multiple_of(void *arg)
   tt_i64_op(round_int64_to_next_multiple_of(INT64_MIN,2), ==, INT64_MIN);
   tt_i64_op(round_int64_to_next_multiple_of(INT64_MAX,2), ==,
                                             INT64_MAX-INT64_MAX%2);
+
+  tt_assert(round_uint32_to_next_multiple_of(0,1) == 0);
+  tt_assert(round_uint32_to_next_multiple_of(0,7) == 0);
+
+  tt_assert(round_uint32_to_next_multiple_of(99,1) == 99);
+  tt_assert(round_uint32_to_next_multiple_of(99,7) == 105);
+  tt_assert(round_uint32_to_next_multiple_of(99,9) == 99);
+
+  tt_assert(round_uint32_to_next_multiple_of(UINT32_MAX,2) ==
+            UINT32_MAX-UINT32_MAX%2);
+
+  tt_assert(round_to_next_multiple_of(0,1) == 0);
+  tt_assert(round_to_next_multiple_of(0,7) == 0);
+
+  tt_assert(round_to_next_multiple_of(99,1) == 99);
+  tt_assert(round_to_next_multiple_of(99,7) == 105);
+  tt_assert(round_to_next_multiple_of(99,9) == 99);
+
+  tt_assert(round_to_next_multiple_of(UINT_MAX,2) ==
+            UINT_MAX-UINT_MAX%2);
  done:
   ;
 }