diff --git a/codex-rs/tui/src/app/snapshots/codex_tui__app__owned_transcript__tests__conversation_in_offset_rect.snap b/codex-rs/tui/src/app/snapshots/codex_tui__app__owned_transcript__tests__conversation_in_offset_rect.snap
index 58eceddd64..d18190e127 100644
--- a/codex-rs/tui/src/app/snapshots/codex_tui__app__owned_transcript__tests__conversation_in_offset_rect.snap
+++ b/codex-rs/tui/src/app/snapshots/codex_tui__app__owned_transcript__tests__conversation_in_offset_rect.snap
@@ -4,14 +4,14 @@ expression: normalize_snapshot_paths(screen)
 ---
 ····································
 ····································
-·····                          ·····
 ·····› Second prompt           ·····
 ·····                          ·····
 ·····                          ·····
 ·····• For the complete        ·····
 ·····  instructions see the    ·····
-·····  manual (https://        ·····
-·····  example.com/docs).      ·····
+·····  manual                  ·····
+·····  (https://example.com/doc·····
+·····  s).                     ·····
 ·····                          ·····
 ·····                          ·····
 ·····› preserved draft         ·····
diff --git a/codex-rs/tui/src/markdown_render.rs b/codex-rs/tui/src/markdown_render.rs
index 69459f7243..d06cd5c05e 100644
--- a/codex-rs/tui/src/markdown_render.rs
+++ b/codex-rs/tui/src/markdown_render.rs
@@ -2396,6 +2396,11 @@ impl<'a, 'policy> Writer<'a, 'policy> {
         if let Some(mut line) = self.current_line_content.take() {
             let style = self.current_line_style;
             let mut source = crate::terminal_hyperlinks::LogicalLineSource::from_line(&line.line);
+            if !self.current_line_in_code_block
+                && crate::wrapping::text_contains_url_like(&source.text)
+            {
+                source.wrap_policy = crate::terminal_hyperlinks::LineWrapPolicy::UrlAware;
+            }
             source.copy = Some(std::sync::Arc::new(std::mem::take(&mut self.copy_line)));
             // NB we don't wrap code in code blocks, in order to preserve whitespace for copy/paste.
             if !self.current_line_in_code_block
diff --git a/codex-rs/tui/src/transcript_view/copy_on_select_tests.rs b/codex-rs/tui/src/transcript_view/copy_on_select_tests.rs
index 1f8bcd30c9..ab4c7affef 100644
--- a/codex-rs/tui/src/transcript_view/copy_on_select_tests.rs
+++ b/codex-rs/tui/src/transcript_view/copy_on_select_tests.rs
@@ -186,7 +186,7 @@ fn copy_on_select_preserves_link_activation_and_ignores_empty_drags() {
             copy_on_select: true,
             ..Default::default()
         };
-        render(&mut view, &cells, /*width*/ 30, /*height*/ 1);
+        render(&mut view, &cells, /*width*/ 30, /*height*/ 2);
         let down = mouse(MouseEventKind::Down(MouseButton::Left), /*column*/ 2);
         assert!(matches!(
             view.handle_mouse(down, &cells),
diff --git a/codex-rs/tui/src/transcript_view/text_tests.rs b/codex-rs/tui/src/transcript_view/text_tests.rs
index 464bfe610c..e017b13007 100644
--- a/codex-rs/tui/src/transcript_view/text_tests.rs
+++ b/codex-rs/tui/src/transcript_view/text_tests.rs
@@ -298,6 +298,29 @@ fn narrow_wrapping_keeps_joined_emoji_whole() {
     assert_eq!(buffer[(0, 0)].symbol(), "👩‍💻");
 }
 
+#[test]
+fn fullscreen_markdown_keeps_a_fitting_url_on_one_row() {
+    use crate::history_cell::AgentMarkdownCell;
+    use crate::history_cell::HistoryCell;
+    let cell = AgentMarkdownCell::new(
+        "See the documentation at https://example.com/docs/reference.".into(),
+        std::path::Path::new("."),
+    );
+    let layout = TextLayout::new(
+        cell.retained_hyperlink_lines(/*width*/ 44, /*detailed*/ false),
+        /*width*/ 44,
+    );
+    let rows = layout
+        .rows
+        .iter()
+        .map(|row| row.line.line.to_string())
+        .collect::<Vec<_>>();
+    insta::assert_snapshot!(rows.join("\n"), @"
+    • See the documentation at
+      https://example.com/docs/reference.
+    ");
+}
+
 #[test]
 fn source_backed_markdown_copy_preserves_code_indentation() {
     use crate::history_cell::AgentMarkdownCell;