diff --git a/openmmtools/multistate/multistatesampler.py b/openmmtools/multistate/multistatesampler.py
index 37d8588c..55b8e3c0 100644
--- a/openmmtools/multistate/multistatesampler.py
+++ b/openmmtools/multistate/multistatesampler.py
@@ -660,13 +660,47 @@ def equilibrate(self, n_iterations, mcmc_moves=None):
             raise RuntimeError('The number of MCMCMoves ({}) and ThermodynamicStates ({}) for equilibration'
                                ' must be the same.'.format(len(self._mcmc_moves), self.n_states))
 
+        timer = utils.Timer()
+        timer.start('Run Equilibration')
+
         # Temporarily set the equilibration MCMCMoves.
         production_mcmc_moves = self._mcmc_moves
         self._mcmc_moves = mcmc_moves
-        for iteration in range(n_iterations):
+        for iteration in range(1, 1 + n_iterations):
             logger.debug("Equilibration iteration {}/{}".format(iteration, n_iterations))
+            timer.start('Equilibration Iteration')
+
+            # NOTE: Unlike run(), do NOT increment iteration counter.
+            # self._iteration += 1
+
+            # Propagate replicas.
             self._propagate_replicas()
 
+            # Compute energies of all replicas at all states
+            self._compute_energies()
+
+            # Update thermodynamic states
+            self._mix_replicas()
+
+            # Computing timing information
+            iteration_time = timer.stop('Equilibration Iteration')
+            partial_total_time = timer.partial('Run Equilibration')
+            time_per_iteration = partial_total_time / iteration
+            estimated_time_remaining = time_per_iteration * (n_iterations - iteration)
+            estimated_total_time = time_per_iteration * n_iterations
+            estimated_finish_time = time.time() + estimated_time_remaining
+            # TODO: Transmit timing information
+
+            # Show timing statistics if debug level is activated.
+            if logger.isEnabledFor(logging.DEBUG):
+                logger.debug("Iteration took {:.3f}s.".format(iteration_time))
+                if estimated_time_remaining != float('inf'):
+                    logger.debug("Estimated completion (of equilibration only) in {}, at {} (consuming total wall clock time {}).".format(
+                        str(datetime.timedelta(seconds=estimated_time_remaining)),
+                        time.ctime(estimated_finish_time),
+                        str(datetime.timedelta(seconds=estimated_total_time))))
+        timer.report_timing()
+
         # Restore production MCMCMoves.
         self._mcmc_moves = production_mcmc_moves
 
diff --git a/openmmtools/multistate/sams.py b/openmmtools/multistate/sams.py
index b1417412..b39fad1f 100644
--- a/openmmtools/multistate/sams.py
+++ b/openmmtools/multistate/sams.py
@@ -426,11 +426,13 @@ def _mix_replicas(self):
         logger.debug("Accepted {}/{} attempted swaps ({:.1f}%)".format(n_swaps_accepted, n_swaps_proposed,
                                                                        swap_fraction_accepted * 100.0))
 
-        # Update logZ estimates
-        self._update_logZ_estimates(replicas_log_P_k)
+        # Do not update and/or write to disk during equilibration
+        if self._iteration > 0:
+            # Update logZ estimates
+            self._update_logZ_estimates(replicas_log_P_k)
 
-        # Update log weights based on target probabilities
-        self._update_log_weights()
+            # Update log weights based on target probabilities
+            self._update_log_weights()
 
     def _local_jump(self, replicas_log_P_k):
         n_replica, n_states, locality = self.n_replicas, self.n_states, self.locality
diff --git a/openmmtools/tests/test_sampling.py b/openmmtools/tests/test_sampling.py
index 821b739b..631da5c0 100644
--- a/openmmtools/tests/test_sampling.py
+++ b/openmmtools/tests/test_sampling.py
@@ -1178,8 +1178,8 @@ def test_equilibrate(self):
             if len(node_replica_ids) == n_replicas:
                 reporter = self.REPORTER(storage_path, open_mode='r', checkpoint_interval=1)
                 stored_sampler_states = reporter.read_sampler_states(iteration=0)
-                for new_state, stored_state in zip(sampler._sampler_states, stored_sampler_states):
-                    assert np.allclose(new_state.positions, stored_state.positions)
+                for stored_state in stored_sampler_states:
+                    assert any([np.allclose(new_state.positions, stored_state.positions) for new_state in sampler._sampler_states])
 
             # We are still at iteration 0.
             assert sampler._iteration == 0