diff --git a/crates/time/src/format.rs b/crates/time/src/format.rs
index a5f4a1a..b595031 100644
--- a/crates/time/src/format.rs
+++ b/crates/time/src/format.rs
@@ -143,6 +143,15 @@ mod tests {
         assert_eq!(format_position(12345, TimeFormat::Samples, sr, &map, rate, 0), "12345");
     }
 
+    #[test]
+    fn minimum_bar_parses_without_overflow() {
+        let (sr, map, rate) = ctx();
+        let p = |t: &str| parse_position(t, TimeFormat::BarsBeats, sr, &map, rate, 0);
+        assert!(p("-9223372036854775808|01|000").is_ok_and(|s| s < 0));
+        assert_eq!(p("2|3|000").ok(), Some(144_000));
+        assert_eq!(p("0|1|000").ok(), Some(-96_000));
+    }
+
     #[test]
     fn parse_round_trips() {
         let (sr, map, rate) = ctx();
diff --git a/crates/time/src/tempo.rs b/crates/time/src/tempo.rs
index 5b87a3a..b9948f9 100644
--- a/crates/time/src/tempo.rs
+++ b/crates/time/src/tempo.rs
@@ -200,7 +200,7 @@ impl TempoMap {
         let mut cur_tick = 0i64;
         let first = self.meter_at_tick(0);
         if bar < 1 {
-            return (bar - 1).saturating_mul(first.ticks_per_bar());
+            return bar.saturating_sub(1).saturating_mul(first.ticks_per_bar());
         }
         for (i, m) in self.meters.iter().enumerate() {
             let next_tick = self.meters.get(i + 1).map(|n| n.tick);
@@ -288,6 +288,13 @@ mod tests {
         assert_eq!(m.bar_beat_at(24_000, sr), BarBeat { bar: 1, beat: 2, tick: 0 });
     }
 
+    #[test]
+    fn minimum_bar_saturates_instead_of_overflowing() {
+        let m = TempoMap::default();
+        assert_eq!(m.bar_start_tick(i64::MIN), i64::MIN);
+        assert_eq!(m.bar_start_tick(0), -TICKS_PER_QUARTER * 4);
+    }
+
     #[test]
     fn tempo_change_is_integrated() {
         let mut m = TempoMap::default();