diff --git a/crates/core/src/addr.rs b/crates/core/src/addr.rs
index 2bdfe797a..2c087f22e 100644
--- a/crates/core/src/addr.rs
+++ b/crates/core/src/addr.rs
@@ -210,11 +210,18 @@ impl RangeRef {
             if let (Some(x), Some(y)) = (CellRef::parse(a), CellRef::parse(b)) {
                 return Some(RangeRef::new(x, y));
             }
-            let strip = |t: &str| t.trim_start_matches('$').to_string();
+            let strip = |t: &str| t.strip_prefix('$').unwrap_or(t).to_string();
             if let (Some(x), Some(y)) = (letters_to_col(&strip(a)), letters_to_col(&strip(b))) {
                 return Some(RangeRef::cols(x.min(y), x.max(y)));
             }
-            let (pa, pb) = (strip(a).parse::<u32>().ok()?, strip(b).parse::<u32>().ok()?);
+            let row_num = |t: &str| {
+                let t = t.strip_prefix('$').unwrap_or(t);
+                if t.is_empty() || !t.bytes().all(|c| c.is_ascii_digit()) {
+                    return None;
+                }
+                t.parse::<u32>().ok()
+            };
+            let (pa, pb) = (row_num(a)?, row_num(b)?);
             if pa == 0 || pb == 0 || pa > MAX_ROWS || pb > MAX_ROWS {
                 return None;
             }
@@ -234,6 +241,18 @@ impl fmt::Display for RangeRef {
 mod tests {
     use super::*;
 
+    #[test]
+    fn range_parse_rejects_signed_rows() {
+        assert!(RangeRef::parse("+1:+3").is_none());
+        assert!(RangeRef::parse("-1:3").is_none());
+        assert!(RangeRef::parse("$$1:3").is_none());
+        assert!(RangeRef::parse(":3").is_none());
+        assert!(RangeRef::parse("$$A:$$C").is_none());
+        assert!(RangeRef::parse("$A:$C").is_some());
+        let r = RangeRef::parse("$1:$3").unwrap();
+        assert_eq!((r.start.row, r.end.row), (0, 2));
+    }
+
     #[test]
     fn letters_roundtrip() {
         for (c, s) in [(0, "A"), (25, "Z"), (26, "AA"), (51, "AZ"), (52, "BA"), (701, "ZZ"), (702, "AAA"), (16383, "XFD")] {