diff --git a/cgt/__init__.py b/cgt/__init__.py
index ddcdb42..c1c5a3e 100644
--- a/cgt/__init__.py
+++ b/cgt/__init__.py
@@ -18,4 +18,7 @@
 from .position_paradigm import GenomeFramework, PositionParadigmFramework, Framework
 from .models import Model
 from . import distances
-from . import plotting
\ No newline at end of file
+from . import plotting
+import warnings
+# This is required because we have complex numbers arising from numerical error that we want to ignore
+warnings.filterwarnings("ignore", message="ComplexWarning")
\ No newline at end of file
diff --git a/cgt/distances.py b/cgt/distances.py
index f5403e6..813bff0 100644
--- a/cgt/distances.py
+++ b/cgt/distances.py
@@ -516,6 +516,24 @@ def min_distance(framework, model, genome_instances=None, weighted=False):
     }
 
 
+def fast_min_distance(framework, model, genome_instances=None):
+    num_genomes = int(
+        framework.genome_group().order() / framework.symmetry_group().order()
+    )
+    if genome_instances is None:
+        genomes = list(framework.genomes().keys())
+        genome_instances = genomes
+    dists = {}
+    for rep in genome_instances:
+        stepwise_dists = fast_step_probabilities(framework, model)[rep]
+        def a(k):
+            return stepwise_dists[k]
+        for k in range(0, num_genomes):
+            if a(k) > 10 ** (-10):
+                dists[rep] = k
+                break
+    return dists
+
 def min_distance_using_irreps(framework, model, genome_instances=None):
     num_genomes = int(
         framework.genome_group().order() / framework.symmetry_group().order()
@@ -646,6 +664,7 @@ def get_distance_function(distance_type):
         case DISTANCE.MFPT: return fast_MFPT
         case DISTANCE.discrete_MFPT: return discrete_MFPT
         case DISTANCE.min: return min_distance_using_irreps
+        case DISTANCE.min_exact: return fast_min_distance
         case DISTANCE.MLE: return mles
         case DISTANCE.min_weighted: return min_distance
 
@@ -682,6 +701,8 @@ def distance_matrix(
         D[i, j] = distances[need_distances[p]]
 
     if replace_nan_with != np.nan:
+        if replace_nan_with == 'max':
+            replace_nan_with = D.max() + 0.1
         D[np.isnan(D)] = replace_nan_with
 
     return D
diff --git a/cgt/enums.py b/cgt/enums.py
index 1fa91b6..f22de93 100644
--- a/cgt/enums.py
+++ b/cgt/enums.py
@@ -73,6 +73,7 @@ class DISTANCE(Enum):
     MFPT = mean_first_passage_time = auto()
     MLE = maximum_likelihood_distance = maximum_likelihood_estimate = auto()
     discrete_MFPT = DMFPT = discrete_mean_first_passage_time = auto()
+    min_exact = auto()
 
 class DATA(Enum):
     eig_data = 'eigen_data'
diff --git a/cgt/simulations.py b/cgt/simulations.py
index 5b01d15..22bc304 100644
--- a/cgt/simulations.py
+++ b/cgt/simulations.py
@@ -19,7 +19,7 @@ def newick_to_tree(newick_string):
     return tree
 
 
-def evolve_on_tree(tree, framework, model, root="random", at_least_one_change=False, exactly_n_changes=None):
+def evolve_on_tree(tree, framework, model, root="random", at_least_one_change=False, exactly_n_changes=None, exactly_bl_changes=False):
     # The tree should be a networkx DiGraph
     # Choose a genome at the root of the tree
     if root == "random":
@@ -43,6 +43,8 @@ def evolve_on_tree(tree, framework, model, root="random", at_least_one_change=Fa
         # Decide how many rearrangements to apply
         if exactly_n_changes is not None:
             num_rearrangements = exactly_n_changes
+        elif exactly_bl_changes:
+            num_rearrangements = int(branch_length)
         else:
             num_rearrangements = np.random.poisson(branch_length)
         if at_least_one_change:
diff --git a/plot.pdf b/plot.pdf
index b007443..19af546 100644
Binary files a/plot.pdf and b/plot.pdf differ