diff --git a/crates/engine/src/lib.rs b/crates/engine/src/lib.rs
index e8e586cf..14802b27 100644
--- a/crates/engine/src/lib.rs
+++ b/crates/engine/src/lib.rs
@@ -660,6 +660,7 @@ impl Session {
         let d = if metric { Drawing::new_metric() } else { Drawing::new_imperial() };
         let mut st = DocState::new(d, &format!("Drawing{}", self.untitled_counter), None);
         st.set_view_quiet(if metric { View { center: Vec2::new(210.0, 148.5), height: 297.0 } } else { View::default() });
+        self.end_running();
         self.docs.push(st);
         self.active = self.docs.len() - 1;
         self.active
@@ -673,10 +674,18 @@ impl Session {
                 height: (ext.height().max(ext.width() * self.viewport_px.1 / self.viewport_px.0.max(1.0)) * 1.1).max(1e-6),
             });
         }
+        self.end_running();
         self.docs.push(st);
         self.active = self.docs.len() - 1;
         self.active
     }
+    /// A command still waiting for input belongs to the drawing it started in: end it there
+    /// before another drawing becomes current, so its undo step lands in that drawing.
+    fn end_running(&mut self) {
+        if self.running.is_some() {
+            self.cancel();
+        }
+    }
 
     pub fn state(&self) -> Result<&DocState> {
         self.docs.get(self.active).ok_or(EngineError::NoDocument)
diff --git a/crates/engine/tests/new_open_end_command.rs b/crates/engine/tests/new_open_end_command.rs
new file mode 100644
index 00000000..d978b0fe
--- /dev/null
+++ b/crates/engine/tests/new_open_end_command.rs
@@ -0,0 +1,82 @@
+//! NEW and OPEN end a command left waiting for input (#715): it belongs to the drawing it started
+//! in, so its changes are undone there, and undo in the new drawing never brings back the other.
+
+use cadcraft_engine::Session;
+use cadcraft_engine::cmd::file::{IoHooks, set_io};
+use cadcraft_engine::doc::Drawing;
+use serde_json::json;
+
+fn count(s: &Session) -> usize {
+    s.doc().unwrap().entity_count()
+}
+
+/// LINE with one segment drawn, still asking for the next point.
+fn line_running(s: &mut Session) {
+    s.cmdline("line").unwrap();
+    s.cmdline("0,0").unwrap();
+    s.cmdline("1,1").unwrap();
+    assert!(s.running.is_some());
+    assert_eq!(count(s), 1);
+}
+
+/// Draw a line in the current drawing, undo it and check what is left.
+fn line_then_undo(s: &mut Session, title: &str, left: usize) {
+    s.cmdline("line").unwrap();
+    s.cmdline("0,0").unwrap();
+    s.cmdline("5,5").unwrap();
+    s.cmdline("").unwrap();
+    assert_eq!(count(s), left + 1);
+    s.undo().unwrap();
+    assert_eq!(s.state().unwrap().title, title);
+    assert_eq!(count(s), left, "undo restores this drawing, not the other one");
+}
+
+/// The first drawing kept its segment, and its own undo removes it.
+fn first_drawing_keeps_its_line(s: &mut Session) {
+    s.execute("document.switch", &json!({"index": 0})).unwrap();
+    assert_eq!(count(s), 1);
+    s.undo().unwrap();
+    assert_eq!(count(s), 0);
+}
+
+#[test]
+fn new_ends_the_command_of_the_previous_drawing() {
+    let mut s = Session::new();
+    line_running(&mut s);
+    s.execute("new", &json!({"metric": true})).unwrap();
+    assert!(s.running.is_none(), "LINE ends with its drawing");
+    assert_eq!(count(&s), 0);
+    line_then_undo(&mut s, "Drawing2", 0);
+    first_drawing_keeps_its_line(&mut s);
+}
+
+fn two_circles(_: &[u8], _: &str) -> Result<Drawing, String> {
+    let mut s = Session::new();
+    for x in [0, 10] {
+        s.execute("circle", &json!({"center": [x, 0], "radius": 1})).unwrap();
+    }
+    Ok(s.doc().unwrap().clone())
+}
+
+#[test]
+fn open_ends_the_command_of_the_previous_drawing() {
+    set_io(IoHooks { read: two_circles, write: |_, _| Err("no writer in tests".into()), plot: None });
+    let mut s = Session::new();
+    line_running(&mut s);
+    s.execute("open", &json!({"data": "AA==", "name": "Circles.dxf"})).unwrap();
+    assert!(s.running.is_none(), "LINE ends with its drawing");
+    assert_eq!(count(&s), 2);
+    line_then_undo(&mut s, "Circles.dxf", 2);
+    first_drawing_keeps_its_line(&mut s);
+}
+
+#[test]
+fn new_without_a_command_keeps_the_selection_of_the_previous_drawing() {
+    let mut s = Session::new();
+    s.execute("circle", &json!({"center": [0, 0], "radius": 1})).unwrap();
+    s.execute("selectall", &json!({})).unwrap();
+    let selected = s.selection();
+    assert_eq!(selected.len(), 1);
+    s.execute("new", &json!({"metric": true})).unwrap();
+    assert_eq!(s.docs[0].selection, selected);
+}