diff --git a/src/combinator/mod.rs b/src/combinator/mod.rs
index fe6655b98..df847f5e8 100644
--- a/src/combinator/mod.rs
+++ b/src/combinator/mod.rs
@@ -869,8 +869,8 @@ where
 
 /// Creates an iterator from input data and a parser.
 ///
-/// Call the iterator's [ParserIterator::finish] method to get the remaining input if successful,
-/// or the error value if we encountered an error.
+/// Call the iterator's [ParserIterator::finish] method to get the remaining
+/// input if successful, or the error value if we encountered an error.
 ///
 /// On [`Err::Error`], iteration will stop. To instead chain an error up, see [`cut`].
 ///
@@ -887,7 +887,7 @@ where
 /// assert_eq!(parsed, [("abc", 3usize), ("defg", 4), ("hijkl", 5), ("mnopqr", 6)].iter().cloned().collect());
 /// assert_eq!(res, Ok(("123", ())));
 /// ```
-pub fn iterator<Input, Error, F>(input: Input, f: F) -> ParserIterator<Input, Error, F>
+pub fn iterator<Input, Error, F>(input: Input, f: F) -> ParserIterator<Input, Error, F, Streaming>
 where
   F: Parser<Input>,
   Error: ParseError<Input>,
@@ -895,21 +895,40 @@ where
   ParserIterator {
     iterator: f,
     input,
-    state: Some(State::Running),
+    state: State::Running,
+    _streaming: PhantomData,
+  }
+}
+
+/// Same as [iterator] but for complete parsers
+pub fn iterator_complete<Input, Error, F>(
+  input: Input,
+  f: F,
+) -> ParserIterator<Input, Error, F, Complete>
+where
+  F: Parser<Input>,
+  Error: ParseError<Input>,
+{
+  ParserIterator {
+    iterator: f,
+    input,
+    state: State::Running,
+    _streaming: PhantomData,
   }
 }
 
 /// Main structure associated to the [iterator] function.
-pub struct ParserIterator<I, E, F> {
+pub struct ParserIterator<I, E, F, S> {
   iterator: F,
   input: I,
-  state: Option<State<E>>,
+  state: State<E>,
+  _streaming: std::marker::PhantomData<S>,
 }
 
-impl<I: Clone, E, F> ParserIterator<I, E, F> {
+impl<I: Clone, E, F, S> ParserIterator<I, E, F, S> {
   /// Returns the remaining input if parsing was successful, or the error if we encountered an error.
-  pub fn finish(mut self) -> IResult<I, (), E> {
-    match self.state.take().unwrap() {
+  pub fn finish(self) -> IResult<I, (), E> {
+    match self.state {
       State::Running | State::Done => Ok((self.input, ())),
       State::Failure(e) => Err(Err::Failure(e)),
       State::Incomplete(i) => Err(Err::Incomplete(i)),
@@ -917,33 +936,33 @@ impl<I: Clone, E, F> ParserIterator<I, E, F> {
   }
 }
 
-impl<Input, Output, Error, F> core::iter::Iterator for ParserIterator<Input, Error, F>
+impl<Input, Output, Error, F, S> core::iter::Iterator for ParserIterator<Input, Error, F, S>
 where
   F: Parser<Input, Output = Output, Error = Error>,
   Input: Clone,
+  S: IsStreaming,
 {
   type Item = Output;
 
   fn next(&mut self) -> Option<Self::Item> {
-    if let State::Running = self.state.take().unwrap() {
+    if let State::Running = self.state {
       let input = self.input.clone();
 
-      match (self.iterator).parse(input) {
+      match (self.iterator).process::<OutputM<Emit, Emit, S>>(input) {
         Ok((i, o)) => {
           self.input = i;
-          self.state = Some(State::Running);
           Some(o)
         }
         Err(Err::Error(_)) => {
-          self.state = Some(State::Done);
+          self.state = State::Done;
           None
         }
         Err(Err::Failure(e)) => {
-          self.state = Some(State::Failure(e));
+          self.state = State::Failure(e);
           None
         }
         Err(Err::Incomplete(i)) => {
-          self.state = Some(State::Incomplete(i));
+          self.state = State::Incomplete(i);
           None
         }
       }