diff --git a/algorithms.py b/algorithms.py
index 55fa82c66..b2d90bdb3 100644
--- a/algorithms.py
+++ b/algorithms.py
@@ -549,6 +549,7 @@ def __init__(
         gene_conversion_rate=0.0,
         gene_conversion_length=1,
         discrete_genome=True,
+        stop_condition=None,
     ):
         # Must be a square matrix.
         N = len(migration_matrix)
@@ -640,6 +641,7 @@ def __init__(
         for time in census_times:
             self.modifier_events.append((time[0], self.census_event, time))
         self.modifier_events.sort()
+        self.stop_condition = stop_condition
 
     def initialise(self, ts):
         root_time = np.max(self.tables.nodes.time)
@@ -684,12 +686,34 @@ def initialise(self, ts):
                     self.set_segment_mass(seg)
                     seg = seg.next
 
+    def get_num_ancestors(self):
+        return sum(pop.get_num_ancestors() for pop in self.P)
+
     def ancestors_remain(self):
         """
         Returns True if the simulation is not finished, i.e., there is some ancestral
         material that has not fully coalesced.
         """
-        return sum(pop.get_num_ancestors() for pop in self.P) != 0
+        return self.get_num_ancestors() != 0
+
+    def assert_stop_condition(self):
+        """
+        Returns true if the simulation is not finished given the global
+        stopping condition that was specified.
+        """
+        if self.stop_condition is None:
+            return self.ancestors_remain()
+        elif self.stop_condition == "grand_mrca":
+            return self.get_num_ancestors() > 1
+        elif self.stop_condition == "all_local_mrcas":
+            return any(num_anc > 1 for num_anc in self.S.values())
+        elif self.stop_condition == "time":
+            return True
+        elif self.stop_condition == "pedigree":
+            return True
+        else:
+            print("Error: unknown stop condition-", self.stop_condition)
+            raise ValueError
 
     def change_population_size(self, pop_id, size):
         self.P[pop_id].set_start_size(size)
@@ -835,16 +859,19 @@ def finalise(self):
     def simulate(self, end_time):
         self.verify()
         if self.model == "hudson":
-            self.hudson_simulate(end_time)
+            ret = self.hudson_simulate(end_time)
         elif self.model == "dtwf":
-            self.dtwf_simulate()
+            ret = self.dtwf_simulate(end_time)
         elif self.model == "fixed_pedigree":
-            self.pedigree_simulate()
+            ret = self.pedigree_simulate(end_time)
         elif self.model == "single_sweep":
-            self.single_sweep_simulate()
+            ret = self.single_sweep_simulate()
         else:
             print("Error: bad model specification -", self.model)
             raise ValueError
+
+        if ret == 2:  # _msprime.EXIT_MAX_TIME:
+            self.t = end_time
         return self.finalise()
 
     def get_potential_destinations(self):
@@ -897,15 +924,14 @@ def hudson_simulate(self, end_time):
         """
         Simulates the algorithm until all loci have coalesced.
         """
+        ret = 0
         infinity = sys.float_info.max
         non_empty_pops = {pop.id for pop in self.P if pop.get_num_ancestors() > 0}
         potential_destinations = self.get_potential_destinations()
 
         # only worried about label 0 below
-        while len(non_empty_pops) > 0:
+        while self.assert_stop_condition():
             self.verify()
-            if self.t >= end_time:
-                break
             # self.print_state()
             re_rate = self.get_total_recombination_rate(label=0)
             t_re = infinity
@@ -948,6 +974,9 @@ def hudson_simulate(self, end_time):
                         mig_dest = k
             min_time = min(t_re, t_ca, t_gcin, t_gc_left, t_mig)
             assert min_time != infinity
+            if self.t + min_time > end_time:
+                ret = 2  # _msprime.MAX_EVENT_TIME
+                break
             if self.t + min_time > self.modifier_events[0][0]:
                 t, func, args = self.modifier_events.pop(0)
                 self.t = t
@@ -992,6 +1021,8 @@ def hudson_simulate(self, end_time):
             X = {pop.id for pop in self.P if pop.get_num_ancestors() > 0}
             assert non_empty_pops == X
 
+        return ret
+
     def single_sweep_simulate(self):
         """
         Does a structed coalescent until end_freq is reached, using
@@ -1099,21 +1130,27 @@ def single_sweep_simulate(self):
             self.set_labels(u, 0)
             self.P[0].add(tmp)
 
-    def pedigree_simulate(self):
+    def pedigree_simulate(self, end_time):
         """
         Simulates through the provided pedigree, stopping at the top.
         """
         self.pedigree = Pedigree(self.tables)
-        self.dtwf_climb_pedigree()
+        ret = self.dtwf_climb_pedigree(end_time)
+        return ret
 
-    def dtwf_simulate(self):
+    def dtwf_simulate(self, end_time):
         """
         Simulates the algorithm until all loci have coalesced.
         """
-        while self.ancestors_remain():
+        ret = 0
+        while self.assert_stop_condition():
+            if self.t + 1 > end_time:
+                ret = 2  # _msprime.EXIT_MAX_TIME
+                break
             self.t += 1
             self.verify()
             self.dtwf_generation()
+        return ret
 
     def dtwf_generation(self):
         """
@@ -1251,13 +1288,14 @@ def process_pedigree_common_ancestors(self, ind, ploid):
         self.flush_edges()
         self.verify()
 
-    def dtwf_climb_pedigree(self):
+    def dtwf_climb_pedigree(self, end_time):
         """
         Simulates transmission of ancestral material through a pre-specified
         pedigree
         """
         assert self.num_populations == 1  # Single pop/pedigree for now
         pop = self.P[0]
+        ret = 0
 
         # Go through the extant lineages and gather the ancestral material
         # into the corresponding pedigree individuals.
@@ -1270,9 +1308,13 @@ def dtwf_climb_pedigree(self):
         # Visit pedigree individuals in time order.
         visit_order = sorted(self.pedigree.individuals, key=lambda x: (x.time, x.id))
         for ind in visit_order:
+            if ind.time > end_time:
+                ret = 2  # _msprime.EXIT_MAX_TIME
+                break
             self.t = ind.time
             for ploid in range(ind.ploidy):
                 self.process_pedigree_common_ancestors(ind, ploid)
+        return ret
 
     def store_arg_edges(self, segment, u=-1):
         if u == -1:
@@ -1810,13 +1852,19 @@ def merge_ancestors(self, H, pop_id, label, new_node_id=-1):
                     j = self.S.floor_key(r_max)
                     self.S[r_max] = self.S[j]
                 # Update the number of extant segments.
-                if self.S[left] == len(X):
+                if self.S[left] == len(X) and self.stop_condition is None:
                     self.S[left] = 0
                     right = self.S.succ_key(left)
                 else:
                     right = left
-                    while right < r_max and self.S[right] != len(X):
-                        self.S[right] -= len(X) - 1
+                    while right < r_max:
+                        if self.S[right] <= len(X):
+                            if self.stop_condition is None:
+                                break
+                            else:
+                                self.S[right] = 1
+                        else:
+                            self.S[right] -= len(X) - 1
                         right = self.S.succ_key(right)
                     alpha = self.alloc_segment(left, right, new_node_id, pop_id)
                 # Update the heaps and make the record.
@@ -1956,13 +2004,19 @@ def merge_two_ancestors(self, population_index, label, x, y, u=-1):
                         j = self.S.floor_key(r_max)
                         self.S[r_max] = self.S[j]
                     # Update the number of extant segments.
-                    if self.S[left] == 2:
+                    if self.S[left] == 2 and self.stop_condition is None:
                         self.S[left] = 0
                         right = self.S.succ_key(left)
                     else:
                         right = left
-                        while right < r_max and self.S[right] != 2:
-                            self.S[right] -= 1
+                        while right < r_max:
+                            if self.S[right] <= 2:
+                                if self.stop_condition is None:
+                                    break
+                                else:
+                                    self.S[right] = 1
+                            else:
+                                self.S[right] -= 1
                             right = self.S.succ_key(right)
                         alpha = self.alloc_segment(
                             left=left,
@@ -2253,6 +2307,10 @@ def run_simulate(args):
     else:
         from_ts = tskit.load(args.from_ts)
         tables = from_ts.dump_tables()
+    if args.stop_condition == "pedigree":
+        end_time = np.max(from_ts.nodes_time)
+    else:
+        end_time = args.end_time
 
     s = Simulator(
         tables=tables,
@@ -2275,8 +2333,9 @@ def run_simulate(args):
         gene_conversion_rate=gc_rate,
         gene_conversion_length=mean_tract_length,
         discrete_genome=args.discrete,
+        stop_condition=args.stop_condition,
     )
-    ts = s.simulate(args.end_time)
+    ts = s.simulate(end_time)
     ts.dump(args.output_file)
     if args.verbose:
         s.print_state()
@@ -2373,6 +2432,9 @@ def add_simulator_arguments(parser):
     parser.add_argument(
         "--end-time", type=float, default=np.inf, help="The end for simulations."
     )
+    parser.add_argument(
+        "--stop-condition", type=str, default=None, help="Global stopping condition"
+    )
 
 
 def main(args=None):
diff --git a/tests/test_algorithms.py b/tests/test_algorithms.py
index ce48c4778..d62e1d16f 100644
--- a/tests/test_algorithms.py
+++ b/tests/test_algorithms.py
@@ -431,3 +431,53 @@ def test_one_gen_pedigree(self, num_founders):
             tables.dump(ts_path)
             ts = self.run_script(f"0 --from-ts {ts_path} -r 1 --model=fixed_pedigree")
         assert len(ts.dump_tables().edges) == 0
+
+    def test_stopping_condition_time(self):
+        end_time = 2.5
+        ts = self.run_script(f"10 --stop-condition=time --end-time={end_time}")
+        assert ts.max_root_time == end_time
+        assert ts.num_samples == 10
+        assert ts.num_trees > 1
+        assert not has_discrete_genome(ts)
+        assert ts.sequence_length == 100
+
+    def test_stopping_condition_all_mrcas(self):
+        ts = self.run_script("10 --stop-condition=all_local_mrcas")
+        roots = [tree.root for tree in ts.trees()]
+        assert len(set(roots)) > 1
+        roots_time = [tree.time(tree.root) for tree in ts.trees()]
+        assert len(set(roots_time)) == 1
+        assert ts.num_samples == 10
+        assert ts.num_trees > 1
+        assert not has_discrete_genome(ts)
+        assert ts.sequence_length == 100
+
+    def test_stopping_condition_grand_mrca(self):
+        ts = self.run_script("10 --stop-condition=grand_mrca")
+        assert ts.num_trees > 1
+        roots = [tree.root for tree in ts.trees()]
+        assert len(set(roots)) == 1
+
+    def test_stopping_condition_pedigree(self):
+        num_founders = 4
+        num_generations = 10
+        tables = simulate_pedigree(
+            num_founders=num_founders, num_generations=num_generations
+        )
+        with tempfile.TemporaryDirectory() as tmpdir:
+            ts_path = pathlib.Path(tmpdir) / "pedigree.trees"
+            tables.dump(ts_path)
+            ts = self.run_script(
+                f"0 --from-ts {ts_path} --model=fixed_pedigree -r 0.1 \
+                --stop-condition=pedigree"
+            )
+        assert ts.num_trees > 1
+        assert ts.max_root_time == num_generations - 1
+
+    def test_stopping_condition_dtwf(self):
+        end_time = 20
+        ts = self.run_script(
+            f"10 --model=dtwf --stop-condition=time --end-time={end_time}"
+        )
+        assert ts.num_trees > 1
+        assert ts.max_root_time == end_time