diff --git a/src/elements/mi/mod.rs b/src/elements/mi/mod.rs
index 6d180d5..45a14b4 100644
--- a/src/elements/mi/mod.rs
+++ b/src/elements/mi/mod.rs
@@ -56,7 +56,7 @@ pub struct IdentBuilder<T> {
 
 impl<T> IdentBuilder<T> {
     /// Set the identifier string for the [`Ident`] element.
-    pub fn ident(self, ident: impl Into<String>) -> IdentBuilder<Uninit> {
+    pub fn ident(self, ident: impl Into<String>) -> IdentBuilder<Init> {
         IdentBuilder {
             ident: Some(ident.into()),
             attributes: self.attributes,
diff --git a/src/lib.rs b/src/lib.rs
index 3bf8ce6..18c94fc 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -125,9 +125,12 @@ impl MathMl {
     }
 
     /// Write this `math` element and its children using the given writer.
-    pub fn write<W: Writer>(&self, writer: &mut W) -> Result<W::Buffer, W::Error> {
+    pub fn write<'writer, W: Writer>(
+        &self,
+        writer: &'writer mut W,
+    ) -> Result<&'writer mut W, W::Error> {
         writer.write_mathml(self)?;
-        Ok(writer.finish())
+        Ok(writer)
     }
 
     /// Render this `math` element and its children using the default renderer.
@@ -135,6 +138,7 @@ impl MathMl {
     /// In this implementation, [`BufMathMlWriter`] is used.
     pub fn render(&self) -> Result<String, <BufMathMlWriter as crate::Writer>::Error> {
         self.write(&mut BufMathMlWriter::default())
+            .map(|w| w.finish())
     }
 }