diff --git a/src/resolvelib/resolvers.py b/src/resolvelib/resolvers.py
index 976608b..e5da798 100644
--- a/src/resolvelib/resolvers.py
+++ b/src/resolvelib/resolvers.py
@@ -99,16 +99,16 @@ def merged_with(self, provider, requirement, parent):
             raise RequirementsConflicted(criterion)
         return criterion
 
-    def excluded_of(self, candidate):
-        """Build a new instance from this, but excluding specified candidate.
+    def excluded_of(self, incompatibilities):
+        """Build a new instance from this, but excluding specified candidates.
 
         Returns the new instance, or None if we still have no valid candidates.
         """
-        cands = self.candidates.excluding(candidate)
+        cands = self.candidates.excluding(incompatibilities)
         if not cands:
             return None
         incompats = list(self.incompatibilities)
-        incompats.append(candidate)
+        incompats.extend(incompatibilities)
         return type(self)(cands, list(self.information), incompats)
 
 
@@ -238,10 +238,25 @@ def _attempt_to_pin_criterion(self, name, criterion):
         # end, signal for backtracking.
         return causes
 
+    def _mark_backtrack_on_state(self, incompatibilities):
+        state = self.state
+        for name, candidates in incompatibilities.items():
+            try:
+                criterion = state.criteria[name]
+            except KeyError:
+                continue
+            criterion = criterion.excluded_of(candidates)
+            if criterion is None:
+                return False
+            state.criteria[name] = criterion
+        return True
+
     def _backtrack(self):
         # Drop the current state, it's known not to work.
         del self._states[-1]
 
+        incompatibilities = collections.defaultdict(list)
+
         # We need at least 2 states here:
         # (a) One to backtrack to.
         # (b) One to restore state (a) to its state prior to candidate-pinning,
@@ -255,19 +270,16 @@ def _backtrack(self):
             except KeyError:
                 continue
             self._r.backtracking(candidate)
+            incompatibilities[name].append(candidate)
+
+            # Mark candidates identified during backtracking as incompatible.
+            if not self._mark_backtrack_on_state(incompatibilities):
+                continue
 
             # Create a new state to work on, with the newly known not-working
             # candidate excluded.
             self._push_new_state()
 
-            # Mark the retracted candidate as incompatible.
-            criterion = self.state.criteria[name].excluded_of(candidate)
-            if criterion is None:
-                # This state still does not work. Try the still previous state.
-                del self._states[-1]
-                continue
-            self.state.criteria[name] = criterion
-
             return True
 
         return False
diff --git a/src/resolvelib/structs.py b/src/resolvelib/structs.py
index 479aad5..bb567ab 100644
--- a/src/resolvelib/structs.py
+++ b/src/resolvelib/structs.py
@@ -95,11 +95,11 @@ def for_preference(self):
         """Provide an candidate iterable for `get_preference()`"""
         return self._factory()
 
-    def excluding(self, candidate):
-        """Create a new `Candidates` instance excluding `candidate`."""
+    def excluding(self, candidates):
+        """Create a new `Candidates` instance excluding `candidates`."""
 
         def factory():
-            return (c for c in self._factory() if c != candidate)
+            return (c for c in self._factory() if c not in candidates)
 
         return type(self)(factory)
 
@@ -129,9 +129,9 @@ def for_preference(self):
         """Provide an candidate iterable for `get_preference()`"""
         return self._sequence
 
-    def excluding(self, candidate):
+    def excluding(self, candidates):
         """Create a new instance excluding `candidate`."""
-        return type(self)([c for c in self._sequence if c != candidate])
+        return type(self)([c for c in self._sequence if c not in candidates])
 
 
 def build_iter_view(matches):
diff --git a/tests/test_structs.py b/tests/test_structs.py
index 39602b4..a920a1e 100644
--- a/tests/test_structs.py
+++ b/tests/test_structs.py
@@ -72,6 +72,7 @@ def test_iter_view_for_preference_based_on_sequence(source):
 def test_itera_view_excluding(source):
     view = build_iter_view(source)
 
-    assert list(view.excluding(0)) == [1]
-    assert list(view.excluding(1)) == [0]
-    assert list(view.excluding(2)) == [0, 1]
+    assert list(view.excluding([0])) == [1]
+    assert list(view.excluding([2])) == [0, 1]
+    assert list(view.excluding([0, 1])) == []
+    assert list(view.excluding([1, 2])) == [0]