diff --git a/CHANGELOG.md b/CHANGELOG.md
index 6d322f0..1805de0 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -10,6 +10,9 @@ New features:
 
 Bugfixes:
 
+- Return zero instead of `NaN` from `Data.Int.rem` when the divisor is zero (#60 by @thomashoneyman).
+- Keep the FFI result of `Data.Int.Bits.zshr` within the signed 32-bit `Int` range (#60 by @thomashoneyman). Shifting a negative input by zero or a multiple of 32 now returns that input instead of converting it to an unsigned number.
+
 Other improvements:
 
 ## [v6.0.1](https://github.com/purescript/purescript-integers/releases/tag/v6.0.1) - 2026-10-17
diff --git a/src/Data/Int.js b/src/Data/Int.js
index 98bedbb..2764ca3 100644
--- a/src/Data/Int.js
+++ b/src/Data/Int.js
@@ -49,7 +49,7 @@ export const quot = function (x) {
 
 export const rem = function (x) {
   return function (y) {
-    return x % y;
+    return (x % y) | 0;
   };
 };
 
diff --git a/src/Data/Int.purs b/src/Data/Int.purs
index fe2a77a..13e8ac0 100644
--- a/src/Data/Int.purs
+++ b/src/Data/Int.purs
@@ -228,6 +228,8 @@ fromStringAs = fromStringAsImpl Just Nothing
 -- | div 2 (-3) == 0
 -- | quot 2 (-3) == 0
 -- | ```
+-- |
+-- | Returns zero when the divisor is zero.
 foreign import quot :: Int -> Int -> Int
 
 -- | The `rem` function provides the remainder after _truncating_ integer
@@ -246,6 +248,9 @@ foreign import quot :: Int -> Int -> Int
 -- | mod 2 (-3) == 2
 -- | rem 2 (-3) == 2
 -- | ```
+-- |
+-- | Returns zero when the divisor is zero, consistent with `quot` and `mod`.
+-- | The quotient/remainder law only applies to nonzero divisors.
 foreign import rem :: Int -> Int -> Int
 
 -- | Raise an Int to the power of another Int.
diff --git a/src/Data/Int/Bits.js b/src/Data/Int/Bits.js
index ddb6225..21299d2 100644
--- a/src/Data/Int/Bits.js
+++ b/src/Data/Int/Bits.js
@@ -32,7 +32,7 @@ export const shr = function (n1) {
 
 export const zshr = function (n1) {
   return function (n2) {
-    return n1 >>> n2;
+    return (n1 >>> n2) | 0;
   };
 };
 
diff --git a/src/Data/Int/Bits.purs b/src/Data/Int/Bits.purs
index 98bc5bc..307c754 100644
--- a/src/Data/Int/Bits.purs
+++ b/src/Data/Int/Bits.purs
@@ -34,6 +34,8 @@ foreign import shl :: Int -> Int -> Int
 foreign import shr :: Int -> Int -> Int
 
 -- | Bitwise zero-fill shift right.
+-- | Only the low five bits of the shift count are used. The result is a signed
+-- | 32-bit `Int`, so shifting by zero (or a multiple of 32) returns the input.
 foreign import zshr :: Int -> Int -> Int
 
 -- | Bitwise NOT.
diff --git a/test/Test/Data/Int.js b/test/Test/Data/Int.js
new file mode 100644
index 0000000..4073aaa
--- /dev/null
+++ b/test/Test/Data/Int.js
@@ -0,0 +1,7 @@
+export const applyIntBinary = function (f) {
+  return function (x) {
+    return function (y) {
+      return f(x)(y);
+    };
+  };
+};
diff --git a/test/Test/Data/Int.purs b/test/Test/Data/Int.purs
index c01cd7d..6bc8f5c 100644
--- a/test/Test/Data/Int.purs
+++ b/test/Test/Data/Int.purs
@@ -3,6 +3,7 @@ module Test.Data.Int (testInt) where
 import Prelude
 
 import Data.Int (binary, ceil, even, floor, fromNumber, fromString, fromStringAs, hexadecimal, octal, odd, parity, pow, quot, radix, rem, round, toNumber, toStringAs)
+import Data.Int.Bits (zshr)
 import Data.Maybe (Maybe(..), fromJust)
 import Data.Number (infinity, nan)
 import Effect (Effect)
@@ -10,6 +11,10 @@ import Effect.Console (log)
 import Partial.Unsafe (unsafePartial)
 import Test.Assert (assert)
 
+-- Keep calls opaque to the compiler's bitwise-operation inliner so these
+-- assertions exercise the library's FFI implementation.
+foreign import applyIntBinary :: (Int -> Int -> Int) -> Int -> Int -> Int
+
 testInt :: Effect Unit
 testInt = do
 
@@ -170,6 +175,43 @@ testInt = do
     go 2 (-3)
     go (-2) (-3)
 
+  log "quot and rem return zero for a zero divisor"
+  let
+    testZeroDivisor x = do
+      assert $ quot x 0 == 0
+      assert $ rem x 0 == 0
+      assert $ applyIntBinary rem x 0 == 0
+  testZeroDivisor 0
+  testZeroDivisor 5
+  testZeroDivisor (-5)
+  testZeroDivisor bottom
+  testZeroDivisor top
+
+  log "rem preserves the dividend's sign"
+  assert $ applyIntBinary rem (-8) 3 == (-2)
+  assert $ applyIntBinary rem 8 (-3) == 2
+  assert $ applyIntBinary rem (-8) (-3) == (-2)
+
+  log "zshr FFI returns signed Ints and masks shift counts to five bits"
+  let
+    testShiftCount count = do
+      assert $ applyIntBinary zshr (-1) count == (-1)
+      assert $ applyIntBinary zshr (-8) count == (-8)
+      assert $ applyIntBinary zshr bottom count == bottom
+      assert $ applyIntBinary zshr top count == top
+  testShiftCount 0
+  testShiftCount 32
+  testShiftCount 64
+  testShiftCount (-32)
+
+  log "zshr zero-fills rather than sign-extends negative inputs"
+  assert $ zshr (-8) 1 == 2147483644
+  assert $ zshr bottom 31 == 1
+  assert $ zshr (-8) 33 == 2147483644
+  assert $ applyIntBinary zshr (-8) 1 == 2147483644
+  assert $ applyIntBinary zshr bottom 31 == 1
+  assert $ applyIntBinary zshr (-8) 33 == 2147483644
+
   log "pow"
   assert $ pow 2 2 == 4
   assert $ pow 5 3 == 125