diff --git a/src/draw_target.rs b/src/draw_target.rs
index 378fe68f..137a01fd 100644
--- a/src/draw_target.rs
+++ b/src/draw_target.rs
@@ -1,3 +1,4 @@
+use std::convert::TryInto;
 use std::io;
 use std::sync::{Arc, RwLock, RwLockWriteGuard};
 use std::time::{Duration, Instant};
@@ -350,7 +351,15 @@ impl RateLimiter {
 
         // We add `new` to `capacity`, subtract one for returning `true` from here,
         // then make sure it does not exceed a maximum of `MAX_BURST`, then store it.
-        self.capacity = Ord::min(MAX_BURST, self.capacity + new as u8 - 1);
+        self.capacity = Ord::min(
+            MAX_BURST,
+            u128::from(self.capacity)
+                .saturating_add(new)
+                .saturating_sub(1)
+                .clamp(0, u8::MAX.into())
+                .try_into()
+                .unwrap(),
+        );
         // Store `prev` for the next iteration after subtracting the `remainder`.
         self.prev = now - Duration::from_nanos(remainder as u64);
         true
diff --git a/src/state.rs b/src/state.rs
index f43c3bce..00d203aa 100644
--- a/src/state.rs
+++ b/src/state.rs
@@ -1,4 +1,5 @@
 use std::borrow::Cow;
+use std::convert::TryInto;
 use std::fmt;
 use std::io;
 use std::sync::atomic::{AtomicU64, AtomicU8, Ordering};
@@ -430,7 +431,15 @@ impl AtomicPosition {
         let (new, remainder) = ((diff / INTERVAL), (diff % INTERVAL));
         // We add `new` to `capacity`, subtract one for returning `true` from here,
         // then make sure it does not exceed a maximum of `MAX_BURST`.
-        capacity = Ord::min(MAX_BURST, capacity + new as u8 - 1);
+        capacity = Ord::min(
+            MAX_BURST,
+            u64::from(capacity)
+                .saturating_add(new)
+                .saturating_sub(1)
+                .clamp(0, u8::MAX.into())
+                .try_into()
+                .unwrap(),
+        );
 
         // Then, we just store `capacity` and `prev` atomically for the next iteration
         self.capacity.store(capacity, Ordering::Release);
@@ -579,4 +588,12 @@ mod tests {
         // Should not panic.
         pb.set_position(0);
     }
+
+    #[test]
+    fn test_atomic_position_large_time_difference() {
+        let atomic_position = AtomicPosition::new();
+        let later = atomic_position.start + Duration::from_nanos(INTERVAL * u64::from(u8::MAX));
+        // Should not panic.
+        atomic_position.allow(later);
+    }
 }