diff --git a/src/_pytask/dag.py b/src/_pytask/dag.py
index f8f9fb9e..07ab23b5 100644
--- a/src/_pytask/dag.py
+++ b/src/_pytask/dag.py
@@ -107,7 +107,8 @@ def pytask_dag_select_execution_dag(session: Session, dag: nx.DiGraph) -> None:
     scheduler = TopologicalSorter.from_dag(dag)
     visited_nodes: set[str] = set()
 
-    for task_signature in scheduler.static_order():
+    while scheduler.is_active():
+        task_signature = scheduler.get_ready()[0]
         if task_signature not in visited_nodes:
             task = dag.nodes[task_signature]["task"]
             have_changed = _have_task_or_neighbors_changed(session, dag, task)
@@ -117,6 +118,7 @@ def pytask_dag_select_execution_dag(session: Session, dag: nx.DiGraph) -> None:
                 dag.nodes[task_signature]["task"].markers.append(
                     Mark("skip_unchanged", (), {})
                 )
+        scheduler.done(task_signature)
 
 
 def _have_task_or_neighbors_changed(
diff --git a/src/_pytask/dag_utils.py b/src/_pytask/dag_utils.py
index ded08d3e..cb359e0c 100644
--- a/src/_pytask/dag_utils.py
+++ b/src/_pytask/dag_utils.py
@@ -62,22 +62,27 @@ def node_and_neighbors(dag: nx.DiGraph, node: str) -> Iterable[str]:
 class TopologicalSorter:
     """The topological sorter class.
 
-    This class allows to perform a topological sort
+    This class allows to perform a topological sort#
+
+    Attributes
+    ----------
+    dag
+        Not the full DAG, but a reduced version that only considers tasks.
+    priorities
+        A dictionary of task names to a priority value. 1 for try first, 0 for the
+        default priority and, -1 for try last.
 
     """
 
     dag: nx.DiGraph
-    dag_backup: nx.DiGraph
     priorities: dict[str, int] = field(factory=dict)
-    _is_prepared: bool = False
-    _nodes_out: set[str] = field(factory=set)
+    _nodes_processing: set[str] = field(factory=set)
+    _nodes_done: set[str] = field(factory=set)
 
     @classmethod
     def from_dag(cls, dag: nx.DiGraph) -> TopologicalSorter:
         """Instantiate from a DAG."""
-        if not dag.is_directed():
-            msg = "Only directed graphs have a topological order."
-            raise ValueError(msg)
+        cls.check_dag(dag)
 
         tasks = [
             dag.nodes[node]["task"] for node in dag.nodes if "task" in dag.nodes[node]
@@ -90,35 +95,46 @@ def from_dag(cls, dag: nx.DiGraph) -> TopologicalSorter:
         }
         task_dag = nx.DiGraph(task_dict).reverse()
 
-        return cls(dag=task_dag, priorities=priorities, dag_backup=task_dag.copy())
+        return cls(dag=task_dag, priorities=priorities)
+
+    @classmethod
+    def from_dag_and_sorter(
+        cls, dag: nx.DiGraph, sorter: TopologicalSorter
+    ) -> TopologicalSorter:
+        """Instantiate a sorter from another sorter and a DAG."""
+        new_sorter = cls.from_dag(dag)
+        new_sorter.done(*sorter._nodes_done)
+        new_sorter._nodes_processing = sorter._nodes_processing
+        return new_sorter
+
+    @staticmethod
+    def check_dag(dag: nx.DiGraph) -> None:
+        if not dag.is_directed():
+            msg = "Only directed graphs have a topological order."
+            raise ValueError(msg)
 
-    def prepare(self) -> None:
-        """Perform some checks before creating a topological ordering."""
         try:
-            nx.algorithms.cycles.find_cycle(self.dag)
+            nx.algorithms.cycles.find_cycle(dag)
         except nx.NetworkXNoCycle:
             pass
         else:
             msg = "The DAG contains cycles."
             raise ValueError(msg)
 
-        self._is_prepared = True
-
     def get_ready(self, n: int = 1) -> list[str]:
         """Get up to ``n`` tasks which are ready."""
-        if not self._is_prepared:
-            msg = "The TopologicalSorter needs to be prepared."
-            raise ValueError(msg)
         if not isinstance(n, int) or n < 1:
             msg = "'n' must be an integer greater or equal than 1."
             raise ValueError(msg)
 
-        ready_nodes = {v for v, d in self.dag.in_degree() if d == 0} - self._nodes_out
+        ready_nodes = {
+            v for v, d in self.dag.in_degree() if d == 0
+        } - self._nodes_processing
         prioritized_nodes = sorted(
             ready_nodes, key=lambda x: self.priorities.get(x, 0)
         )[-n:]
 
-        self._nodes_out.update(prioritized_nodes)
+        self._nodes_processing.update(prioritized_nodes)
 
         return prioritized_nodes
 
@@ -128,23 +144,9 @@ def is_active(self) -> bool:
 
     def done(self, *nodes: str) -> None:
         """Mark some tasks as done."""
-        self._nodes_out = self._nodes_out - set(nodes)
+        self._nodes_processing = self._nodes_processing - set(nodes)
         self.dag.remove_nodes_from(nodes)
-
-    def reset(self) -> None:
-        """Reset an exhausted topological sorter."""
-        if self.dag_backup:
-            self.dag = self.dag_backup.copy()
-        self._is_prepared = False
-        self._nodes_out = set()
-
-    def static_order(self) -> Generator[str, None, None]:
-        """Return a topological order of tasks as an iterable."""
-        self.prepare()
-        while self.is_active():
-            new_task = self.get_ready()[0]
-            yield new_task
-            self.done(new_task)
+        self._nodes_done.update(nodes)
 
 
 def _extract_priorities_from_tasks(tasks: list[PTask]) -> dict[str, int]:
diff --git a/src/_pytask/execute.py b/src/_pytask/execute.py
index c6641710..b7dbd5f8 100644
--- a/src/_pytask/execute.py
+++ b/src/_pytask/execute.py
@@ -72,21 +72,21 @@ def pytask_execute_log_start(session: Session) -> None:
 @hookimpl(trylast=True)
 def pytask_execute_create_scheduler(session: Session) -> TopologicalSorter:
     """Create a scheduler based on topological sorting."""
-    scheduler = TopologicalSorter.from_dag(session.dag)
-    scheduler.prepare()
-    return scheduler
+    return TopologicalSorter.from_dag(session.dag)
 
 
 @hookimpl
 def pytask_execute_build(session: Session) -> bool | None:
     """Execute tasks."""
     if isinstance(session.scheduler, TopologicalSorter):
-        for name in session.scheduler.static_order():
-            task = session.dag.nodes[name]["task"]
+        while session.scheduler.is_active():
+            task_name = session.scheduler.get_ready()[0]
+            task = session.dag.nodes[task_name]["task"]
             report = session.hook.pytask_execute_task_protocol(
                 session=session, task=task
             )
             session.execution_reports.append(report)
+            session.scheduler.done(task_name)
 
             if session.should_stop:
                 return True
diff --git a/tests/test_dag_utils.py b/tests/test_dag_utils.py
index f6c685dd..158322fa 100644
--- a/tests/test_dag_utils.py
+++ b/tests/test_dag_utils.py
@@ -16,6 +16,7 @@
 
 @pytest.fixture()
 def dag():
+    """Create a dag with five nodes in a line."""
     dag = nx.DiGraph()
     for i in range(4):
         task = Task(base_name=str(i), path=Path(), function=None)
@@ -29,7 +30,12 @@ def dag():
 
 @pytest.mark.unit()
 def test_sort_tasks_topologically(dag):
-    topo_ordering = list(TopologicalSorter.from_dag(dag).static_order())
+    sorter = TopologicalSorter.from_dag(dag)
+    topo_ordering = []
+    while sorter.is_active():
+        task_name = sorter.get_ready()[0]
+        topo_ordering.append(task_name)
+        sorter.done(task_name)
     topo_names = [dag.nodes[sig]["task"].name for sig in topo_ordering]
     assert topo_names == [f".::{i}" for i in range(5)]
 
@@ -166,37 +172,33 @@ def test_raise_error_for_cycle_in_graph(dag):
         "115f685b0af2aef0c7317a0b48562f34cfb7a622549562bd3d34d4d948b4fdab",
         "55c6cef62d3e62d5f8fc65bb846e66d8d0d3ca60608c04f6f7b095ea073a7dcf",
     )
-    scheduler = TopologicalSorter.from_dag(dag)
     with pytest.raises(ValueError, match="The DAG contains cycles."):
-        scheduler.prepare()
-
-
-@pytest.mark.unit()
-def test_raise_if_topological_sorter_is_not_prepared(dag):
-    scheduler = TopologicalSorter.from_dag(dag)
-    with pytest.raises(ValueError, match="The TopologicalSorter needs to be prepared."):
-        scheduler.get_ready(1)
+        TopologicalSorter.from_dag(dag)
 
 
 @pytest.mark.unit()
 def test_ask_for_invalid_number_of_ready_tasks(dag):
     scheduler = TopologicalSorter.from_dag(dag)
-    scheduler.prepare()
     with pytest.raises(ValueError, match="'n' must be"):
         scheduler.get_ready(0)
 
 
 @pytest.mark.unit()
-def test_reset_topological_sorter(dag):
-    scheduler = TopologicalSorter.from_dag(dag)
-    scheduler.prepare()
-    name = scheduler.get_ready()[0]
-    scheduler.done(name)
-
-    assert scheduler._is_prepared
-    assert name not in scheduler.dag.nodes
+def test_instantiate_sorter_from_other_sorter(dag):
+    name_to_sig = {dag.nodes[sig]["task"].name: sig for sig in dag.nodes}
 
-    scheduler.reset()
-
-    assert not scheduler._is_prepared
-    assert name in scheduler.dag.nodes
+    scheduler = TopologicalSorter.from_dag(dag)
+    for _ in range(2):
+        task_name = scheduler.get_ready()[0]
+        scheduler.done(task_name)
+    assert scheduler._nodes_done == {name_to_sig[name] for name in (".::0", ".::1")}
+
+    task = Task(base_name="5", path=Path(), function=None)
+    dag.add_node(task.signature, task=Task(base_name="5", path=Path(), function=None))
+    dag.add_edge(name_to_sig[".::4"], task.signature)
+
+    new_scheduler = TopologicalSorter.from_dag_and_sorter(dag, scheduler)
+    while new_scheduler.is_active():
+        task_name = new_scheduler.get_ready()[0]
+        new_scheduler.done(task_name)
+    assert new_scheduler._nodes_done == set(name_to_sig.values()) | {task.signature}