diff --git a/crates/engine/src/lib.rs b/crates/engine/src/lib.rs
index 96e09b57..3086f378 100644
--- a/crates/engine/src/lib.rs
+++ b/crates/engine/src/lib.rs
@@ -344,6 +344,11 @@ fn one_view() -> u8 {
     1
 }
 
+/// `t` as a current time of `comp`: a frame within its duration.
+fn comp_frame_at(comp: &Comp, t: Tick) -> Tick {
+    comp.frame_rate.snap_nearest(t.min(comp.duration - comp.frame_duration()).max(Tick::ZERO))
+}
+
 /// What Copy with Property Links / Copy Expression Only put on the clipboard.
 #[derive(Clone, Debug, PartialEq)]
 pub enum LinkClip {
@@ -860,11 +865,7 @@ impl Session {
 
     pub fn set_time(&mut self, t: Tick) {
         if let Some(c) = self.state.active_comp {
-            let comp = self.project.comp(c);
-            let t = match comp {
-                Some(comp) => comp.frame_rate.snap_nearest(t.clamp(Tick::ZERO, comp.duration - comp.frame_duration())),
-                None => t,
-            };
+            let t = self.project.comp(c).map_or(t, |comp| comp_frame_at(comp, t));
             self.state.times.insert(c, t);
             if self.prefs.general.sync_time_related_items {
                 self.sync_related_times(c, t);
@@ -985,13 +986,21 @@ impl Session {
 
     /// The open compositions, as a project file records them ([`effectcraft_project::SavedView`]).
     pub fn saved_view(&self) -> effectcraft_project::SavedView {
-        effectcraft_project::SavedView { active_comp: self.state.active_comp, open_comps: self.state.open_comps.clone() }
+        let comp_times = self.state.times.iter().filter(|(id, _)| self.project.comp(**id).is_some()).map(|(id, t)| (*id, *t)).collect();
+        effectcraft_project::SavedView { active_comp: self.state.active_comp, open_comps: self.state.open_comps.clone(), comp_times }
     }
 
-    /// Reopen the compositions a project file was saved with (#748). Ids that no longer name a
+    /// Reopen the compositions a project file was saved with (#748), each at its saved current
+    /// time (#1714). Ids that no longer name a
     /// comp are skipped; with none left the project stays on the comp [`Session::replace_project`]
     /// opened (its first), as files from before the view was saved do.
     pub fn restore_view(&mut self, view: &effectcraft_project::SavedView) {
+        for (id, t) in &view.comp_times {
+            if let Some(comp) = self.project.comp(*id) {
+                let t = comp_frame_at(comp, *t);
+                self.state.times.insert(*id, t);
+            }
+        }
         let mut open: Vec<ItemId> = Vec::new();
         for id in view.open_comps.iter().copied().filter(|id| self.project.comp(*id).is_some()) {
             if !open.contains(&id) {
diff --git a/crates/engine/src/tests.rs b/crates/engine/src/tests.rs
index 72133c5d..458583ee 100644
--- a/crates/engine/src/tests.rs
+++ b/crates/engine/src/tests.rs
@@ -686,3 +686,41 @@ fn reopening_a_project_restores_its_active_comp() {
         o.insert("openComps".into(), open);
     }
 }
+
+/// Layer times are saved as exact ticks and read back unchanged, and each comp reopens at the
+/// current time it was saved at, not at 0, where a layer starting later shows nothing (#1714).
+#[test]
+fn reopening_a_project_restores_layer_times_and_current_time() {
+    use effectcraft_time::{FrameRate, Tick};
+    let dir = std::env::temp_dir().join(format!("ec-test-1714-{}", std::process::id()));
+    std::fs::create_dir_all(&dir).unwrap();
+    let path = dir.join("times.ecproj").to_string_lossy().to_string();
+    let mut s = Session::default();
+    s.execute("comp.new", json!({"name": "C", "width": 108, "height": 192, "duration": 60})).unwrap();
+    s.execute("layer.newSolid", json!({"name": "crown"})).unwrap();
+    let cid = s.active_comp_id().unwrap();
+    let comp = std::sync::Arc::make_mut(&mut s.project).comp_mut(cid).unwrap();
+    comp.frame_rate = FrameRate::FPS_59_94;
+    // The layer from the issue: 34f, 315f and 3033f at 59.94 fps.
+    let l = comp.layers.first_mut().unwrap();
+    (l.start_time, l.in_point, l.out_point) = (Tick(144_086_342_400), Tick(1_334_917_584_000), Tick(12_853_349_308_800));
+    s.execute("time.set", json!({"time": 6.0})).unwrap();
+    let t = s.time();
+    s.execute("file.saveAs", json!({"path": path})).unwrap();
+
+    let mut s2 = Session::default();
+    s2.execute("file.open", json!({"path": path})).unwrap();
+    let l = s2.project.comp(cid).unwrap().layers.first().unwrap();
+    assert_eq!((l.start_time, l.in_point, l.out_point), (Tick(144_086_342_400), Tick(1_334_917_584_000), Tick(12_853_349_308_800)));
+    assert_eq!(s2.time(), t);
+    assert!(l.in_point <= s2.time() && s2.time() < l.out_point, "the layer shows at the reopened time");
+    assert!(!s2.is_dirty());
+
+    // A saved time past the comp's end (a hand-edited file) lands on its last frame.
+    let text = std::fs::read_to_string(&path).unwrap().replace(&format!("\"{}\": {}", cid.0, t.0), &format!("\"{}\": {}", cid.0, i64::MAX));
+    std::fs::write(&path, text).unwrap();
+    let mut s3 = Session::default();
+    s3.execute("file.open", json!({"path": path})).unwrap();
+    let c = s3.project.comp(cid).unwrap();
+    assert_eq!(s3.time(), c.frame_rate.snap_nearest(c.duration - c.frame_duration()));
+}
diff --git a/crates/project/src/lib.rs b/crates/project/src/lib.rs
index 16d78216..be35590a 100644
--- a/crates/project/src/lib.rs
+++ b/crates/project/src/lib.rs
@@ -62,6 +62,10 @@ pub struct SavedView {
     /// The open comps (Timeline tabs), in tab order.
     #[serde(skip_serializing_if = "Vec::is_empty")]
     pub open_comps: Vec<ItemId>,
+    /// Each comp's current time, so a project reopens on the frame it was saved at rather than
+    /// at 0, where its layers may not have started yet (#1714).
+    #[serde(skip_serializing_if = "BTreeMap::is_empty")]
+    pub comp_times: BTreeMap<ItemId, Tick>,
 }
 
 /// The view a project file was saved with ([`SavedView`]); empty for older files. Values that
@@ -73,6 +77,8 @@ pub fn saved_view(text: &str) -> SavedView {
         active_comp: Option<serde_json::Value>,
         #[serde(rename = "openComps", default)]
         open_comps: Option<serde_json::Value>,
+        #[serde(rename = "compTimes", default)]
+        comp_times: Option<serde_json::Value>,
     }
     let Ok(m) = serde_json::from_str::<Meta>(text) else { return SavedView::default() };
     SavedView {
@@ -82,6 +88,11 @@ pub fn saved_view(text: &str) -> SavedView {
             .as_ref()
             .and_then(serde_json::Value::as_array)
             .map_or_else(Vec::new, |a| a.iter().filter_map(serde_json::Value::as_u64).map(ItemId).collect()),
+        comp_times: m
+            .comp_times
+            .as_ref()
+            .and_then(serde_json::Value::as_object)
+            .map_or_else(BTreeMap::new, |o| o.iter().filter_map(|(k, v)| Some((ItemId(k.parse().ok()?), Tick(v.as_i64()?)))).collect()),
     }
 }
 
diff --git a/crates/project/src/tests.rs b/crates/project/src/tests.rs
index c19d81ee..4edd8661 100644
--- a/crates/project/src/tests.rs
+++ b/crates/project/src/tests.rs
@@ -173,14 +173,14 @@ fn project_files_name_their_version_and_always_read_back() {
 #[test]
 fn project_files_remember_the_open_comps() {
     let (p, cid) = project_with_layer();
-    let view = crate::SavedView { active_comp: Some(cid), open_comps: vec![cid] };
+    let view = crate::SavedView { active_comp: Some(cid), open_comps: vec![cid], comp_times: [(cid, effectcraft_time::Tick(4_237_833_600))].into() };
     let text = p.to_file_json_with_view(&view).unwrap();
     assert_eq!(crate::saved_view(&text), view);
     assert_eq!(Project::from_json(&text).unwrap(), p, "the view is not part of the project");
     // Files from before #748 have no view; a garbled one is ignored, not an error.
     assert_eq!(crate::saved_view(&p.to_file_json().unwrap()), crate::SavedView::default());
     let odd = text.replacen(&format!("\"activeComp\": {}", cid.0), "\"activeComp\": \"Main\"", 1);
-    assert_eq!(crate::saved_view(&odd), crate::SavedView { active_comp: None, open_comps: vec![cid] });
+    assert_eq!(crate::saved_view(&odd), crate::SavedView { active_comp: None, ..view });
 }
 
 /// The Project panel's "used N times": layers in every comp that use the item directly, a precomp