diff --git a/crates/svg/src/import.rs b/crates/svg/src/import.rs
index c8bfe40a..d7762b50 100644
--- a/crates/svg/src/import.rs
+++ b/crates/svg/src/import.rs
@@ -574,6 +574,9 @@ fn view_box_transform(root: XNode, w: f64, h: f64) -> Affine {
     Affine::translate(((w - vb.w * s) * fx, (h - vb.h * s) * fy)) * Affine::scale(s) * Affine::translate((-vb.x, -vb.y))
 }
 
+/// Most line breaks one absolutely positioned `<tspan>` adds before itself.
+const MAX_TSPAN_LINE_GAP: f64 = 10_000.0;
+
 struct RunBuilder {
     runs: Vec<TextRun>,
     last_y: f64,
@@ -630,7 +633,17 @@ fn collect_runs(ctx: &TextCtx, el: XNode, rb: &mut RunBuilder) {
                 let lead = char_style(ctx, c).effective_leading().max(1e-6);
                 if let Some(y) = c.attribute("y") {
                     let y = first_number(Some(y));
-                    let n = ((y - rb.last_y) / lead).round().max(1.0) as usize;
+                    // One line break per line of baseline gap: none for a tspan on the same baseline
+                    // (a styled or kerned run of the same line), at least one for a tspan placed
+                    // higher up, and capped so that a far-off (or non-finite) y can't ask for billions.
+                    let gap = ((y - rb.last_y) / lead).round();
+                    let n = if !gap.is_finite() {
+                        1
+                    } else if (y - rb.last_y).abs() < lead * 0.5 {
+                        0
+                    } else {
+                        gap.clamp(1.0, MAX_TSPAN_LINE_GAP) as usize
+                    };
                     rb.newline(n);
                     rb.last_y = y;
                 } else if c.attribute("dy").is_some_and(|dy| first_number(Some(dy)) > 1e-9) {
diff --git a/crates/svg/tests/roundtrip.rs b/crates/svg/tests/roundtrip.rs
index 0719bcc4..c5006190 100644
--- a/crates/svg/tests/roundtrip.rs
+++ b/crates/svg/tests/roundtrip.rs
@@ -637,6 +637,38 @@ fn import_text_tspans_and_css() {
     assert_eq!(t.runs[1].style.fill.color().unwrap().to_hex(), "#0000ff");
 }
 
+#[test]
+fn import_tspan_far_below_is_bounded() {
+    // A <tspan y> far below the text's first line is a line break per line of gap, but not without
+    // limit: y="1e15" used to ask for ~7e13 line breaks and aborted the process (out of memory).
+    let d = import_art(
+        r#"<svg xmlns="http://www.w3.org/2000/svg" width="100" height="100">
+        <text x="5" y="20" font-size="12">first<tspan x="5" y="48.8">third</tspan><tspan x="5" y="2000000">far</tspan></text></svg>"#,
+    );
+    let a = art(&d);
+    let NodeKind::Text(t) = &a[0].kind else { panic!() };
+    let text = t.plain_text();
+    // One blank line between "first" and "third" (auto leading 14.4 pt: two lines down).
+    assert!(text.starts_with("first\n\nthird\n"), "{text:?}");
+    assert!(text.ends_with("far"), "{text:?}");
+    let breaks = text.matches('\n').count();
+    assert!(breaks <= 10_002, "{breaks} line breaks");
+}
+
+#[test]
+fn import_tspan_on_the_same_baseline_stays_on_the_line() {
+    // Styled runs positioned on the line's own baseline (as Illustrator writes them, with x and y on
+    // every tspan) are one line, not a line break before each run.
+    let d = import_art(
+        r#"<svg xmlns="http://www.w3.org/2000/svg" width="300" height="100">
+        <text transform="translate(10 40)" font-size="20"><tspan x="0" y="0">Hello </tspan><tspan x="55.6" y="0" fill="red">world</tspan><tspan x="0" y="24">next</tspan></text></svg>"#,
+    );
+    let a = art(&d);
+    let NodeKind::Text(t) = &a[0].kind else { panic!() };
+    assert_eq!(t.plain_text(), "Hello world\nnext");
+    assert_eq!(t.runs.len(), 3);
+}
+
 #[test]
 fn import_invalid_is_error() {
     assert!(import("not svg").is_err());