diff --git a/src/buffer.rs b/src/buffer.rs
index 86dec46afd..d4b0dd11ad 100644
--- a/src/buffer.rs
+++ b/src/buffer.rs
@@ -346,11 +346,13 @@ impl<'a> Cursor<'a> {
         self.span()
     }
 
-    /// Skip over the next token without cloning it. Returns `None` if this
-    /// cursor points to eof.
+    /// Skip over the next token that is not a None-delimited group, without
+    /// cloning it. Returns `None` if this cursor points to eof.
     ///
     /// This method treats `'lifetimes` as a single token.
-    pub(crate) fn skip(self) -> Option<Cursor<'a>> {
+    pub(crate) fn skip(mut self) -> Option<Cursor<'a>> {
+        self.ignore_none();
+
         let len = match self.entry() {
             Entry::End(_) => return None,
 
diff --git a/src/parse.rs b/src/parse.rs
index aafc1a9649..5d0fbc43b8 100644
--- a/src/parse.rs
+++ b/src/parse.rs
@@ -614,11 +614,6 @@ impl<'a> ParseBuffer<'a> {
     /// ```
     pub fn peek2<T: Peek>(&self, token: T) -> bool {
         fn peek2(buffer: &ParseBuffer, peek: fn(Cursor) -> bool) -> bool {
-            if let Some(group) = buffer.cursor().group(Delimiter::None) {
-                if group.0.skip().map_or(false, peek) {
-                    return true;
-                }
-            }
             buffer.cursor().skip().map_or(false, peek)
         }
 
@@ -629,11 +624,6 @@ impl<'a> ParseBuffer<'a> {
     /// Looks at the third-next token in the parse stream.
     pub fn peek3<T: Peek>(&self, token: T) -> bool {
         fn peek3(buffer: &ParseBuffer, peek: fn(Cursor) -> bool) -> bool {
-            if let Some(group) = buffer.cursor().group(Delimiter::None) {
-                if group.0.skip().and_then(Cursor::skip).map_or(false, peek) {
-                    return true;
-                }
-            }
             buffer
                 .cursor()
                 .skip()
diff --git a/tests/test_parse_stream.rs b/tests/test_parse_stream.rs
index 11dc1a6630..3a009b4921 100644
--- a/tests/test_parse_stream.rs
+++ b/tests/test_parse_stream.rs
@@ -136,8 +136,8 @@ fn test_peek_groups() {
         assert!(!input.peek2(Token![::]));
         assert!(input.peek2(Token![!]));
         assert!(input.peek2(token::Group));
-        assert!(!input.peek3(Token![=])); // FIXME
-        assert!(input.peek3(Token![static])); // FIXME
+        assert!(input.peek3(Token![=]));
+        assert!(!input.peek3(Token![static]));
 
         let content;
         parenthesized!(content in input);
@@ -155,8 +155,8 @@ fn test_peek_groups() {
         assert!(input.peek(token::Group));
         assert!(input.peek(Token![!]));
         assert!(input.peek2(Token![=]));
-        assert!(!input.peek3(Token![static])); // FIXME
-        assert!(input.peek2(Token![static])); // FIXME
+        assert!(input.peek3(Token![static]));
+        assert!(!input.peek2(Token![static]));
 
         let _: Token![!] = input.parse()?;