diff --git a/CHANGELOG.md b/CHANGELOG.md
index fe33eee..a40ba3b 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,13 +5,6 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
-## [0.1.3] - TBD
-
-### Changed
-
-- Fixed bug in `psuedo_metrics` when extracting summary statistics data.
-- 
-
 ## [0.1.2] - 2024-06-03
 
 ### Changed
@@ -25,6 +18,7 @@ object wasn't refreshed.
 - Refactored pars of `VIPRS` to cache some recurring computations.
 - Updated `VIPRSBMA` & `VIPRSGridSearch` to only consider models that
 successfully converged.
+- Fixed bug in `psuedo_metrics` when extracting summary statistics data.
 
 ### Added
 
@@ -32,6 +26,7 @@ successfully converged.
 - Added measure of time taken to prepare data in `viprs_fit`.
 - Added option to keep long-range LD regions in `viprs_fit`.
 - Added convergence check based on parameter values.
+- Added `min_iter` parameter to `.fit` methods to ensure CAVI is run for at least `min_iter` iterations.
 - Added separate method for initializing optimization-related objects.
 
 ## [0.1.1] - 2024-04-24
diff --git a/benchmarks/benchmark_e_step.py b/benchmarks/benchmark_e_step.py
index b42a6ec..5ff4e6e 100644
--- a/benchmarks/benchmark_e_step.py
+++ b/benchmarks/benchmark_e_step.py
@@ -68,7 +68,9 @@ def exec_func():
         # Here, we roughly repeat until the total time is at least ~1 second:
         # Note that the minimum number of calls is 5. If this takes too long,
         # then set the number of calls manually?
-        time_iter = math.ceil(1. / np.mean(timeit.repeat(exec_func, number=5, repeat=5)))
+        time_iter = math.ceil(1. / np.median(
+            timeit.repeat(exec_func, repeat=5 + warm_up, number=5)[warm_up:]
+        ))
         n_calls = 5 * int(time_iter)
 
     with ResourceProfiler(dt=0.1) as rprof:
diff --git a/viprs/model/VIPRS.py b/viprs/model/VIPRS.py
index 7820a2a..e7672bc 100644
--- a/viprs/model/VIPRS.py
+++ b/viprs/model/VIPRS.py
@@ -730,7 +730,7 @@ def fit(self,
             theta_0=None,
             param_0=None,
             continued=False,
-            min_iter=5,
+            min_iter=3,
             f_abs_tol=1e-6,
             x_abs_tol=1e-7,
             drop_r_tol=0.01,
@@ -801,18 +801,17 @@ def fit(self,
                 curr_elbo = self.history['ELBO'][-1]
                 prev_elbo = self.history['ELBO'][-2]
 
-                if i > min_iter:
-                    # Check for convergence in the objective + parameters:
-                    if np.isclose(prev_elbo, curr_elbo, atol=f_abs_tol, rtol=0.):
-                        self.optim_result.update(curr_elbo,
-                                                 stop_iteration=True,
-                                                 success=True,
-                                                 message='Objective (ELBO) converged successfully.')
-                    elif max([np.max(np.abs(diff)) for diff in self.eta_diff.values()]) < x_abs_tol:
-                        self.optim_result.update(curr_elbo,
-                                                 stop_iteration=True,
-                                                 success=True,
-                                                 message='Variational parameters converged successfully.')
+                # Check for convergence in the objective + parameters:
+                if (i > min_iter) & np.isclose(prev_elbo, curr_elbo, atol=f_abs_tol, rtol=0.):
+                    self.optim_result.update(curr_elbo,
+                                             stop_iteration=True,
+                                             success=True,
+                                             message='Objective (ELBO) converged successfully.')
+                elif (i > min_iter) & max([np.max(np.abs(diff)) for diff in self.eta_diff.values()]) < x_abs_tol:
+                    self.optim_result.update(curr_elbo,
+                                             stop_iteration=True,
+                                             success=True,
+                                             message='Variational parameters converged successfully.')
 
                 # Check to see if the objective drops due to numerical instabilities:
                 elif curr_elbo < prev_elbo and not np.isclose(curr_elbo, prev_elbo, atol=0., rtol=drop_r_tol):
diff --git a/viprs/model/gridsearch/VIPRSGrid.py b/viprs/model/gridsearch/VIPRSGrid.py
index 620f788..821e0bd 100644
--- a/viprs/model/gridsearch/VIPRSGrid.py
+++ b/viprs/model/gridsearch/VIPRSGrid.py
@@ -334,19 +334,19 @@ def fit(self,
 
                 for m in np.where(self.active_models)[0]:
 
-                    if i > min_iter:
-                        if np.isclose(prev_elbo[m], curr_elbo[m], atol=f_abs_tol, rtol=0.):
-                            self.active_models[m] = False
-                            self.optim_results[m].update(curr_elbo[m],
-                                                         stop_iteration=True,
-                                                         success=True,
-                                                         message='Objective (ELBO) converged successfully.')
-                        elif max([np.max(np.abs(diff[:, m])) for diff in self.eta_diff.values()]) < x_abs_tol:
-                            self.active_models[m] = False
-                            self.optim_results[m].update(curr_elbo[m],
-                                                         stop_iteration=True,
-                                                         success=True,
-                                                         message='Variational parameters converged successfully.')
+                    if (i > min_iter) & np.isclose(prev_elbo[m], curr_elbo[m], atol=f_abs_tol, rtol=0.):
+                        self.active_models[m] = False
+                        self.optim_results[m].update(curr_elbo[m],
+                                                     stop_iteration=True,
+                                                     success=True,
+                                                     message='Objective (ELBO) converged successfully.')
+                    elif (i > min_iter) & max([np.max(np.abs(diff[:, m]))
+                                               for diff in self.eta_diff.values()]) < x_abs_tol:
+                        self.active_models[m] = False
+                        self.optim_results[m].update(curr_elbo[m],
+                                                     stop_iteration=True,
+                                                     success=True,
+                                                     message='Variational parameters converged successfully.')
 
                     # Check to see if the objective drops due to numerical instabilities:
                     elif curr_elbo[m] < prev_elbo[m] and not np.isclose(curr_elbo[m],