diff --git a/attic/rabfe/estimator.py b/attic/rabfe/estimator.py
index 005703411..3261e4aa9 100644
--- a/attic/rabfe/estimator.py
+++ b/attic/rabfe/estimator.py
@@ -345,7 +345,7 @@ def deltaG_from_results(
         fwd_delta_u = model.beta * delta_Us[lambda_idx][0]
         rev_delta_u = model.beta * delta_Us[lambda_idx][1]
 
-        dG_exact, exact_bar_err = bar_with_bootstrapped_uncertainty(fwd_delta_u, rev_delta_u)
+        dG_exact, exact_bar_err = bar_with_pessimistic_uncertainty(fwd_delta_u, rev_delta_u)
 
         bar_dG += dG_exact / model.beta
         exact_bar_overlap = endpoint_correction.overlap_from_cdf(fwd_delta_u, rev_delta_u)
@@ -407,7 +407,7 @@ def deltaG_from_results(
             rhs_xs=results[-1].xs,
             seed=2021,
         )
-        dG_endpoint, endpoint_err = bar_with_bootstrapped_uncertainty(
+        dG_endpoint, endpoint_err = bar_with_pessimistic_uncertainty(
             model.beta * lhs_du, model.beta * np.array(rhs_du)
         )
         dG_endpoint = dG_endpoint / model.beta
diff --git a/tests/data/zero_overlap_ukln.npz b/tests/data/zero_overlap_ukln.npz
new file mode 100644
index 000000000..fe8f3de67
Binary files /dev/null and b/tests/data/zero_overlap_ukln.npz differ
diff --git a/tests/test_bar.py b/tests/test_bar.py
index 417c7184d..eb174ff16 100644
--- a/tests/test_bar.py
+++ b/tests/test_bar.py
@@ -1,5 +1,7 @@
 from functools import partial
+from pathlib import Path
 from typing import Tuple
+from unittest.mock import patch
 
 import numpy as np
 import pymbar
@@ -8,7 +10,7 @@
 from pymbar.testsystems import ExponentialTestCase
 
 from timemachine.fe.bar import (
-    bar_with_bootstrapped_uncertainty,
+    bar_with_pessimistic_uncertainty,
     bootstrap_bar,
     compute_fwd_and_reverse_df_over_time,
     df_and_err_from_u_kln,
@@ -83,8 +85,14 @@ def test_bootstrap_bar(sigma):
 
     # estimate 3 times
     df_ref, df_err_ref = df_and_err_from_u_kln(u_kln)
-    df_0, bootstrap_samples = bootstrap_bar(u_kln, n_bootstrap=n_bootstrap)
-    df_1, bootstrap_sigma = bar_with_bootstrapped_uncertainty(u_kln)
+    df_0, ddf_0, bootstrap_samples = bootstrap_bar(u_kln, n_bootstrap=n_bootstrap)
+    df_1, bootstrap_sigma = bar_with_pessimistic_uncertainty(u_kln)
+
+    # Full errors should match exactly
+    assert df_err_ref == ddf_0
+
+    # The bootstrapped error should be as large or larger than the full error
+    assert bootstrap_sigma >= df_err_ref
 
     # assert estimates identical, uncertainties comparable
     print(f"bootstrap uncertainty = {bootstrap_sigma}, pymbar.MBAR uncertainty = {df_err_ref}")
@@ -216,3 +224,31 @@ def test_compute_fwd_and_reverse_df_over_time(frames_per_step):
     # The values at the end should be nearly identical since they contain all the samples
     assert np.allclose(fwd[-1], rev[-1])
     assert np.allclose(fwd_err[-1], rev_err[-1])
+
+
+def test_bootstrap_bar_and_regular_bar_match():
+    """In cases where the u_kln has effectively no overlap, bootstrapping returns 0.0
+    since the MBAR estimate is always zero. Checks that `bar_with_pessimistic_uncertainty` returns the (non-zero) error
+    from the MBAR estimate computed on all samples in these cases.
+    """
+    test_ukln = Path(__file__).parent / "data" / "zero_overlap_ukln.npz"
+    u_kln = np.load(open(test_ukln, "rb"))["u_kln"]
+
+    # The overlap should be closer to zero
+    overlap = pair_overlap_from_ukln(u_kln)
+    np.testing.assert_allclose(overlap, 0.0, atol=1e-12)
+
+    boot_df, boot_df_err = bar_with_pessimistic_uncertainty(u_kln)
+    df, df_err = df_and_err_from_u_kln(u_kln)
+    assert boot_df == df
+    assert boot_df_err == df_err
+
+
+@patch("timemachine.fe.bar.pymbar.MBAR.getFreeEnergyDifferences")
+def test_nan_bar_error(mock_energy_diff):
+    df = np.zeros(shape=(1, 2))
+    df_err = np.ones(shape=(1, 2)) * np.nan
+    mock_energy_diff.return_value = (df, df_err)
+    dummy_ukln = np.ones(shape=(2, 2, 100))
+    _, boot_df_err = bar_with_pessimistic_uncertainty(dummy_ukln)
+    assert boot_df_err == 0.0
diff --git a/tests/test_fe_absolute_hydration.py b/tests/test_fe_absolute_hydration.py
index 0d8e49fe5..f02640c32 100644
--- a/tests/test_fe_absolute_hydration.py
+++ b/tests/test_fe_absolute_hydration.py
@@ -19,7 +19,7 @@ def test_run_solvent():
 
     assert res.plots.overlap_summary_png is not None
     assert res.plots.overlap_detail_png is not None
-    assert np.linalg.norm(res.final_result.dG_errs) < 10
+    assert np.linalg.norm(res.final_result.dG_errs) < 20.0
     assert len(res.frames) == n_windows
     assert len(res.boxes) == n_windows
     assert len(res.frames[0]) == n_frames
diff --git a/timemachine/fe/bar.py b/timemachine/fe/bar.py
index dfc2d2d12..4f33712cd 100644
--- a/timemachine/fe/bar.py
+++ b/timemachine/fe/bar.py
@@ -151,7 +151,7 @@ def df_from_u_kln(
 
 def bootstrap_bar(
     u_kln: NDArray, n_bootstrap: int = 100, maximum_iterations: int = DEFAULT_MAXIMUM_ITERATIONS
-) -> Tuple[float, NDArray]:
+) -> Tuple[float, float, NDArray]:
     """Given a 2-state u_kln matrix, subsample u_kln with replacement and re-run df_from_u_kln many times
 
     Parameters
@@ -166,8 +166,12 @@ def bootstrap_bar(
     Returns
     -------
     best_estimate : float
-        BAR(w_F, w_R, computeUncertainty=False)
-    bootstrap_samples: array
+        BAR(w_F, w_R)
+
+    best_estimate_err : float
+        MBAR(w_F, w_R) error estimate, using all samples
+
+    bootstrap_samples : array
         shape (n_bootstrap,)
 
     Notes
@@ -178,7 +182,9 @@ def bootstrap_bar(
     u_kn, N_k = ukln_to_ukn(u_kln)
     mbar = pymbar.MBAR(u_kn, N_k, maximum_iterations=maximum_iterations)
 
-    full_bar_result = mbar.getFreeEnergyDifferences(compute_uncertainty=False)[0][0, 1]
+    df, ddf = mbar.getFreeEnergyDifferences()
+    full_bar_result = df[0, 1]
+    full_bar_err = ddf[0, 1]
 
     _, _, n = u_kln.shape
 
@@ -196,15 +202,34 @@ def bootstrap_bar(
         )
         bootstrap_samples.append(bar_result)
 
-    return full_bar_result, np.array(bootstrap_samples)
+    return full_bar_result, full_bar_err, np.array(bootstrap_samples)
 
 
-def bar_with_bootstrapped_uncertainty(
+def bar_with_pessimistic_uncertainty(
     u_kln: NDArray, n_bootstrap=100, maximum_iterations: int = DEFAULT_MAXIMUM_ITERATIONS
 ) -> Tuple[float, float]:
-    """Given 2-state u_kln, returns free energy difference and uncertainty computed by bootstrapping."""
+    """Given 2-state u_kln, returns free energy difference and the uncertainty. The uncertainty can be produced either by
+    BAR using all samples or the bootstrapped error, whichever is greater.
+
+    Parameters
+    ----------
+    u_kln : array
+        2-state u_kln matrix
+    n_bootstrap : int
+        number of bootstrap samples
+    maximum_iterations : int
+        maximum number of solver iterations to use for each sample
+
+    Returns
+    -------
+    best_estimate : float
+        BAR(w_F, w_R)
+
+    uncertainty : float
+        `max(error_estimates)` where `error_estimates = [bootstrapped_bar_stddev, two_state_mbar_uncertainty]`
+    """
 
-    df, bootstrap_dfs = bootstrap_bar(u_kln, n_bootstrap=n_bootstrap, maximum_iterations=maximum_iterations)
+    df, ddf, bootstrap_dfs = bootstrap_bar(u_kln, n_bootstrap=n_bootstrap, maximum_iterations=maximum_iterations)
 
     # warn if bootstrap distribution deviates significantly from normality
     normaltest_result = normaltest(bootstrap_dfs)
@@ -212,8 +237,12 @@ def bar_with_bootstrapped_uncertainty(
     if normaltest_result.pvalue < pvalue_threshold:
         logger.warning(f"bootstrapped errors non-normal: {normaltest_result}")
 
-    # regardless, summarize as if normal
-    ddf = np.std(bootstrap_dfs)
+    # Take the max of the BAR error estimate using all samples and the bootstrapped error. Summarize as if normal regardless
+    # Use np.maximum to always return the NaN
+    if not np.isfinite(ddf):
+        logger.warning(f"BAR error estimate is not finite, setting to zero: {ddf}")
+        ddf = 0.0
+    ddf = np.maximum(ddf, np.std(bootstrap_dfs))
     return df, ddf
 
 
diff --git a/timemachine/fe/free_energy.py b/timemachine/fe/free_energy.py
index 967a28987..4c5d742ba 100644
--- a/timemachine/fe/free_energy.py
+++ b/timemachine/fe/free_energy.py
@@ -10,7 +10,7 @@
 from timemachine.constants import BOLTZ
 from timemachine.fe import model_utils, topology
 from timemachine.fe.bar import (
-    bar_with_bootstrapped_uncertainty,
+    bar_with_pessimistic_uncertainty,
     df_and_err_from_u_kln,
     pair_overlap_from_ukln,
     works_from_ukln,
@@ -696,7 +696,7 @@ def estimate_free_energy_bar(u_kln_by_component: NDArray, temperature: float) ->
 
     u_kln = u_kln_by_component.sum(0)
 
-    df, df_err = bar_with_bootstrapped_uncertainty(u_kln)  # reduced units
+    df, df_err = bar_with_pessimistic_uncertainty(u_kln)  # reduced units
 
     kBT = BOLTZ * temperature
     dG, dG_err = df * kBT, df_err * kBT  # kJ/mol