diff --git a/src/duration.rs b/src/duration.rs
index 59bfa00b74..6e29e28bed 100644
--- a/src/duration.rs
+++ b/src/duration.rs
@@ -350,6 +350,15 @@ impl Duration {
         }
         Ok(StdDuration::new(self.secs as u64, self.nanos as u32))
     }
+
+    /// This duplicates `Neg::neg` because trait methods can't be const yet.
+    pub(crate) const fn neg(self) -> Duration {
+        if self.nanos == 0 {
+            Duration { secs: -self.secs, nanos: 0 }
+        } else {
+            Duration { secs: -self.secs - 1, nanos: NANOS_PER_SEC - self.nanos }
+        }
+    }
 }
 
 impl Neg for Duration {
diff --git a/src/naive/time/mod.rs b/src/naive/time/mod.rs
index f6861c0385..b47639ce0d 100644
--- a/src/naive/time/mod.rs
+++ b/src/naive/time/mod.rs
@@ -639,8 +639,8 @@ impl NaiveTime {
     /// ```
     #[inline]
     #[must_use]
-    pub fn overflowing_sub_signed(&self, rhs: OldDuration) -> (NaiveTime, i64) {
-        let (time, rhs) = self.overflowing_add_signed(-rhs);
+    pub const fn overflowing_sub_signed(&self, rhs: OldDuration) -> (NaiveTime, i64) {
+        let (time, rhs) = self.overflowing_add_signed(rhs.neg());
         (time, -rhs) // safe to negate, rhs is within +/- (2^63 / 1000)
     }