diff --git a/src/domains.rs b/src/domains.rs
index 92c2eb3..f65a740 100644
--- a/src/domains.rs
+++ b/src/domains.rs
@@ -98,6 +98,9 @@ pub(crate) fn find_authority_end(
     let mut chars = s.char_indices();
 
     while let Some((i, c)) = chars.next() {
+        if require_host && !userinfo_allowed && !maybe_host {
+            break;
+        }
         let can_be_last = match c {
             // ALPHA
             'a'..='z' | 'A'..='Z' | '\u{80}'..=char::MAX => {
diff --git a/tests/domains.rs b/tests/domains.rs
index f8c7f44..5d9b2c0 100644
--- a/tests/domains.rs
+++ b/tests/domains.rs
@@ -181,6 +181,15 @@ pub fn test_international_allowed() {
     assert_eq!(link.as_str(), "\u{A1}\u{A2}example.com");
 }
 
+#[test]
+fn no_quadratic_scan_of_schemeless_hosts() {
+    // Each `~` makes the current candidate invalid as a host. Scanning has to stop there
+    // instead of running to the end of the input for every candidate, otherwise this test
+    // takes hours instead of milliseconds.
+    let input = "a.a~".repeat(2_000_000);
+    assert_not_linked(&input);
+}
+
 fn assert_linked(input: &str, expected: &str) {
     let mut finder = LinkFinder::new();
     finder.url_must_have_scheme(false);