diff --git a/Cargo.lock b/Cargo.lock
index 4041e19..4e3a036 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -1150,9 +1150,9 @@ dependencies = [
 
 [[package]]
 name = "pulldown-cmark"
-version = "0.12.2"
+version = "0.13.4"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "f86ba2052aebccc42cbbb3ed234b8b13ce76f75c3551a303cb2bcffcff12bb14"
+checksum = "e9f068eba8e7071c5f9511831b44f32c740d5adf574e990f946ddb53db2f314e"
 dependencies = [
  "bitflags 2.12.1",
  "getopts",
diff --git a/Cargo.toml b/Cargo.toml
index b653fb2..289d54a 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -31,7 +31,7 @@ unicode-width = "0.2"
 # `pulldown-cmark` renders inline markdown for terminal display, while
 # `markdown` provides the mdast/source-structure parser used by selection and
 # AST views. Keeping both is intentional until one parser can satisfy both jobs.
-pulldown-cmark = "0.12"
+pulldown-cmark = "0.13"
 markdown = "1"
 
 [dev-dependencies]
diff --git a/src/markdown.rs b/src/markdown.rs
index 6c31380..ca9ca5c 100644
--- a/src/markdown.rs
+++ b/src/markdown.rs
@@ -220,6 +220,10 @@ impl MarkdownLineRenderer {
             MdTag::Emphasis => self.emphasis_depth += 1,
             MdTag::Strong => self.strong_depth += 1,
             MdTag::Strikethrough => self.strike_depth += 1,
+            // These extensions remain disabled in `markdown_options`, so they
+            // should not normally be emitted. Handle their wrappers explicitly
+            // to stay compatible with pulldown-cmark 0.13.
+            MdTag::Superscript | MdTag::Subscript => {}
             MdTag::Table(_)
             | MdTag::TableHead
             | MdTag::TableRow
@@ -270,6 +274,7 @@ impl MarkdownLineRenderer {
             TagEnd::Emphasis => self.emphasis_depth = self.emphasis_depth.saturating_sub(1),
             TagEnd::Strong => self.strong_depth = self.strong_depth.saturating_sub(1),
             TagEnd::Strikethrough => self.strike_depth = self.strike_depth.saturating_sub(1),
+            TagEnd::Superscript | TagEnd::Subscript => {}
             TagEnd::Paragraph
             | TagEnd::Item
             | TagEnd::DefinitionList
@@ -412,6 +417,7 @@ impl MarkdownLineRenderer {
 #[cfg(test)]
 mod tests {
     use super::render_markdown_line;
+    use ratatui::style::Modifier;
 
     #[test]
     fn renders_markdown_headings() {
@@ -432,4 +438,21 @@ mod tests {
         assert_eq!(rendered.plain, line);
         assert_eq!(rendered.spans.len(), 1);
     }
+
+    #[test]
+    fn superscript_stays_literal_and_single_tilde_stays_struck_out() {
+        let rendered = render_markdown_line("H^2^O and ~CO~");
+        assert_eq!(rendered.plain, "H^2^O and CO");
+        let carbon_monoxide = rendered
+            .spans
+            .iter()
+            .find(|span| span.content == "CO")
+            .expect("single-tilde content should be rendered");
+        assert!(
+            carbon_monoxide
+                .style
+                .add_modifier
+                .contains(Modifier::CROSSED_OUT)
+        );
+    }
 }