diff --git a/CHANGELOG.md b/CHANGELOG.md
index fe2ce0756..f04823150 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -43,7 +43,7 @@ The format is based on [Keep a Changelog]. This project adheres to [Semantic Ver
 
 - Cross-building to Windows now succeeds.
 - A parse error on a `UtcOffset` component now indicates the error comes from the offset.
-- `Duration::checked_sub` and `Duration::saturating_sub` no longer panic in edge cases.
+- Some arithmetic no longer panics in edge cases.
 
 ## 0.3.3 [2021-09-25]
 
diff --git a/src/date.rs b/src/date.rs
index df8e206fe..1bf7e14ae 100644
--- a/src/date.rs
+++ b/src/date.rs
@@ -742,7 +742,8 @@ impl Sub<Duration> for Date {
     type Output = Self;
 
     fn sub(self, duration: Duration) -> Self::Output {
-        self + -duration
+        Self::from_julian_day(self.to_julian_day() - duration.whole_days() as i32)
+            .expect("overflow subtracting duration to date")
     }
 }
 
diff --git a/src/instant.rs b/src/instant.rs
index a1f79a152..9b422fb22 100644
--- a/src/instant.rs
+++ b/src/instant.rs
@@ -89,7 +89,14 @@ impl Instant {
     /// assert_eq!(now.checked_sub((-5).seconds()), Some(now - (-5).seconds()));
     /// ```
     pub fn checked_sub(self, duration: Duration) -> Option<Self> {
-        self.checked_add(-duration)
+        if duration.is_zero() {
+            Some(self)
+        } else if duration.is_positive() {
+            self.0.checked_sub(duration.abs_std()).map(Self)
+        } else {
+            debug_assert!(duration.is_negative());
+            self.0.checked_add(duration.abs_std()).map(Self)
+        }
     }
     // endregion checked arithmetic
 
@@ -186,7 +193,13 @@ impl Sub<Duration> for Instant {
     type Output = Self;
 
     fn sub(self, duration: Duration) -> Self::Output {
-        self + -duration
+        if duration.is_positive() {
+            Self(self.0 - duration.abs_std())
+        } else if duration.is_negative() {
+            Self(self.0 + duration.abs_std())
+        } else {
+            self
+        }
     }
 }
 
diff --git a/src/primitive_date_time.rs b/src/primitive_date_time.rs
index 8ade2b16f..ac0281a4e 100644
--- a/src/primitive_date_time.rs
+++ b/src/primitive_date_time.rs
@@ -605,7 +605,21 @@ impl Sub<Duration> for PrimitiveDateTime {
     type Output = Self;
 
     fn sub(self, duration: Duration) -> Self::Output {
-        self + -duration
+        let (date_adjustment, time) = self.time.adjusting_sub(duration);
+        let date = self.date - duration;
+
+        Self {
+            date: match date_adjustment {
+                util::DateAdjustment::Previous => date
+                    .previous_day()
+                    .expect("resulting value is out of range"),
+                util::DateAdjustment::Next => {
+                    date.next_day().expect("resulting value is out of range")
+                }
+                util::DateAdjustment::None => date,
+            },
+            time,
+        }
     }
 }
 
diff --git a/src/time.rs b/src/time.rs
index aa7952b42..494ea9c53 100644
--- a/src/time.rs
+++ b/src/time.rs
@@ -328,8 +328,8 @@ impl Time {
     // endregion getters
 
     // region: arithmetic helpers
-    /// Add the sub-day time of the [`Duration`] to the `Time`. Wraps on overflow, returning the
-    /// necessary whether the date is the following day.
+    /// Add the sub-day time of the [`Duration`] to the `Time`. Wraps on overflow, returning whether
+    /// the date is different.
     pub(crate) const fn adjusting_add(self, duration: Duration) -> (DateAdjustment, Self) {
         let mut nanoseconds = self.nanosecond as i32 + duration.subsec_nanoseconds();
         let mut seconds = self.second as i8 + (duration.whole_seconds() % 60) as i8;
@@ -359,6 +359,37 @@ impl Time {
         )
     }
 
+    /// Subtract the sub-day time of the [`Duration`] to the `Time`. Wraps on overflow, returning
+    /// whether the date is different.
+    pub(crate) const fn adjusting_sub(self, duration: Duration) -> (DateAdjustment, Self) {
+        let mut nanoseconds = self.nanosecond as i32 - duration.subsec_nanoseconds();
+        let mut seconds = self.second as i8 - (duration.whole_seconds() % 60) as i8;
+        let mut minutes = self.minute as i8 - (duration.whole_minutes() % 60) as i8;
+        let mut hours = self.hour as i8 - (duration.whole_hours() % 24) as i8;
+        let mut date_adjustment = DateAdjustment::None;
+
+        cascade!(nanoseconds in 0..1_000_000_000 => seconds);
+        cascade!(seconds in 0..60 => minutes);
+        cascade!(minutes in 0..60 => hours);
+        if hours >= 24 {
+            hours -= 24;
+            date_adjustment = DateAdjustment::Next;
+        } else if hours < 0 {
+            hours += 24;
+            date_adjustment = DateAdjustment::Previous;
+        }
+
+        (
+            date_adjustment,
+            Self::__from_hms_nanos_unchecked(
+                hours as _,
+                minutes as _,
+                seconds as _,
+                nanoseconds as _,
+            ),
+        )
+    }
+
     /// Add the sub-day time of the [`std::time::Duration`] to the `Time`. Wraps on overflow,
     /// returning whether the date is the previous date as the first element of the tuple.
     pub(crate) const fn adjusting_add_std(self, duration: StdDuration) -> (bool, Self) {
@@ -524,7 +555,7 @@ impl Sub<Duration> for Time {
     /// assert_eq!(time!(23:59:59) - (-2).seconds(), time!(0:00:01));
     /// ```
     fn sub(self, duration: Duration) -> Self::Output {
-        self + -duration
+        self.adjusting_sub(duration).1
     }
 }
 
diff --git a/tests/integration/instant.rs b/tests/integration/instant.rs
index b0a2dee03..cc993e3e7 100644
--- a/tests/integration/instant.rs
+++ b/tests/integration/instant.rs
@@ -121,6 +121,7 @@ fn add_assign_std_duration() {
 fn sub_duration() {
     let instant = Instant::now();
     assert!(instant - 100.milliseconds() <= Instant::now());
+    assert_eq!(instant - Duration::ZERO, instant);
 }
 
 #[test]