diff --git a/neo4j/work/result.py b/neo4j/work/result.py
index 6465a65d..c449a5d8 100644
--- a/neo4j/work/result.py
+++ b/neo4j/work/result.py
@@ -28,6 +28,7 @@
     SessionExpired,
 )
 from neo4j.work.summary import ResultSummary
+from neo4j.exceptions import ResultConsumedError
 
 
 class _ConnectionErrorHandler:
@@ -223,20 +224,37 @@ def __iter__(self):
         self._closed = True
 
     def _attach(self):
-        """Sets the Result object in an attached state by fetching messages from the connection to the buffer.
+        """Sets the Result object in an attached state by fetching messages from
+        the connection to the buffer.
         """
         if self._closed is False:
             while self._attached is False:
                 self._connection.fetch_message()
 
-    def _buffer_all(self):
-        """Sets the Result object in an detached state by fetching all records from the connection to the buffer.
+    def _buffer(self, n=None):
+        """Try to fill `self_record_buffer` with n records.
+
+        Might end up with more records in the buffer if the fetch size makes it
+        overshoot.
+        Might ent up with fewer records in the buffer if there are not enough
+        records available.
         """
         record_buffer = deque()
         for record in self:
             record_buffer.append(record)
+            if n is not None and len(record_buffer) >= n:
+                break
         self._closed = False
-        self._record_buffer = record_buffer
+        if n is None:
+            self._record_buffer = record_buffer
+        else:
+            self._record_buffer.extend(record_buffer)
+
+    def _buffer_all(self):
+        """Sets the Result object in an detached state by fetching all records
+        from the connection to the buffer.
+        """
+        self._buffer()
 
     def _obtain_summary(self):
         """Obtain the summary of this result, buffering any remaining records.
@@ -309,6 +327,13 @@ def single(self):
         :returns: the next :class:`neo4j.Record` or :const:`None` if none remain
         :warns: if more than one record is available
         """
+        # TODO in 5.0 replace with this code that raises an error if there's not
+        # exactly one record in the left result stream.
+        # self._buffer(2).
+        # if len(self._record_buffer) != 1:
+        #     raise SomeError("Expected exactly 1 record, found %i"
+        #                      % len(self._record_buffer))
+        # return self._record_buffer.popleft()
         records = list(self)  # TODO: exhausts the result with self.consume if there are more records.
         size = len(records)
         if size == 0:
@@ -323,16 +348,9 @@ def peek(self):
 
         :returns: the next :class:`.Record` or :const:`None` if none remain
         """
+        self._buffer(1)
         if self._record_buffer:
             return self._record_buffer[0]
-        if not self._attached:
-            return None
-        while self._attached:
-            self._connection.fetch_message()
-            if self._record_buffer:
-                return self._record_buffer[0]
-
-        return None
 
     def graph(self):
         """Return a :class:`neo4j.graph.Graph` instance containing all the graph objects
diff --git a/tests/unit/work/test_result.py b/tests/unit/work/test_result.py
index d7f49ece..936d3be8 100644
--- a/tests/unit/work/test_result.py
+++ b/tests/unit/work/test_result.py
@@ -272,12 +272,14 @@ def test_result_peek(records, fetch_size):
     connection = ConnectionStub(records=Records(["x"], records))
     result = Result(connection, HydratorStub(), fetch_size, noop, noop)
     result._run("CYPHER", {}, None, "r", None)
-    record = result.peek()
-    if not records:
-        assert record is None
-    else:
-        assert isinstance(record, Record)
-        assert record.get("x") == records[0][0]
+    for i in range(len(records) + 1):
+        record = result.peek()
+        if i == len(records):
+            assert record is None
+        else:
+            assert isinstance(record, Record)
+            assert record.get("x") == records[i][0]
+            next(iter(result))  # consume the record
 
 
 @pytest.mark.parametrize("records", ([[1], [2]], [[1]], []))