diff --git a/regex-syntax/src/hir/mod.rs b/regex-syntax/src/hir/mod.rs
index e5ea3701b..062d4dcab 100644
--- a/regex-syntax/src/hir/mod.rs
+++ b/regex-syntax/src/hir/mod.rs
@@ -2481,16 +2481,24 @@ impl Properties {
             props.literal = props.literal && p.is_literal();
             props.alternation_literal =
                 props.alternation_literal && p.is_alternation_literal();
-            if let Some(ref mut minimum_len) = props.minimum_len {
+            if let Some(minimum_len) = props.minimum_len {
                 match p.minimum_len() {
                     None => props.minimum_len = None,
-                    Some(len) => *minimum_len += len,
+                    Some(len) => {
+                        // We use saturating arithmetic here because the
+                        // minimum is just a lower bound. We can't go any
+                        // higher than what our number types permit.
+                        props.minimum_len =
+                            Some(minimum_len.saturating_add(len));
+                    }
                 }
             }
-            if let Some(ref mut maximum_len) = props.maximum_len {
+            if let Some(maximum_len) = props.maximum_len {
                 match p.maximum_len() {
                     None => props.maximum_len = None,
-                    Some(len) => *maximum_len += len,
+                    Some(len) => {
+                        props.maximum_len = maximum_len.checked_add(len)
+                    }
                 }
             }
         }
diff --git a/tests/regression.rs b/tests/regression.rs
index e24fecbc5..1ff4cba9f 100644
--- a/tests/regression.rs
+++ b/tests/regression.rs
@@ -240,3 +240,11 @@ fn regression_unicode_perl_not_enabled() {
     let re = regex_new!(pat);
     assert!(re.is_ok());
 }
+
+// See: https://github.com/rust-lang/regex/issues/995
+#[test]
+fn regression_big_regex_overflow() {
+    let pat = r" {2147483516}{2147483416}{5}";
+    let re = regex_new!(pat);
+    assert!(re.is_err());
+}