diff --git a/CHANGELOG.md b/CHANGELOG.md
index ba9ed33..49e84bd 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -6,6 +6,12 @@ The format follows [Keep a Changelog](https://keepachangelog.com/en/1.1.0/).
 
 ## [Unreleased]
 
+### Added
+
+- Allow adaptive SMC to set `beta_tolerance` independently of the minimum
+  beta increment, including through `make_standard_bayesian_smc`'s
+  `weighting_kwargs`. The default continues to use `min_delta` as the tolerance.
+
 ## [0.1.0] - 2026-10-29
 
 First stable release. Changes below are relative to 0.1.0b1.
diff --git a/src/sequince/prebuilt_samplers.py b/src/sequince/prebuilt_samplers.py
index 0946790..7bb4506 100644
--- a/src/sequince/prebuilt_samplers.py
+++ b/src/sequince/prebuilt_samplers.py
@@ -122,6 +122,9 @@ def make_standard_bayesian_smc(
         Criterion for adaptive tempering; one of ``"ess"`` (default) or ``"cess"``.
     weighting_kwargs : dict[str, Any] or None, optional
         Extra keyword arguments forwarded to the weighting step constructor.
+        For adaptive tempering, ``beta_tolerance`` sets the beta-search
+        precision independently of ``min_delta``; ``max_bisection_iter``
+        limits the number of search iterations.
     resampling : {"systematic", "stratified", "multinomial"}, optional
         Resampling strategy to use; one of ``"systematic"``, ``"stratified"``,
         or ``"multinomial"``.
diff --git a/src/sequince/steps/weighting.py b/src/sequince/steps/weighting.py
index a6c31ab..6d71ace 100644
--- a/src/sequince/steps/weighting.py
+++ b/src/sequince/steps/weighting.py
@@ -783,6 +783,10 @@ class AdaptiveTemperedWeighting(BaseTemperedStep):
     max_bisection_iter:
         The maximum number of bisection iterations to perform when finding
         the beta increment.
+    beta_tolerance : float or None, optional
+        Stop bisection when the beta bracket is no wider than this finite,
+        positive value. Defaults to ``min_delta`` when None, preserving the
+        existing search behavior. Does not change the minimum beta increment.
     criterion:
         Criterion used when selecting the beta increment. ``"ess"``
         targets the ESS ratio after weighting. ``"cess"`` targets the
@@ -805,6 +809,7 @@ def __init__(
         max_delta: float | None = None,
         normalize_after: bool = True,
         max_bisection_iter: int = 30,
+        beta_tolerance: float | None = None,
         criterion: Literal["ess", "cess"] = "ess",
         refresh_components: Collection[str] = (),
     ):
@@ -816,6 +821,10 @@ def __init__(
             raise ValueError("max_beta must be positive.")
         if min_delta < 0.0:
             raise ValueError("min_delta must be non-negative.")
+        if beta_tolerance is not None and (
+            not math.isfinite(beta_tolerance) or beta_tolerance <= 0.0
+        ):
+            raise ValueError("beta_tolerance must be finite and positive.")
         if max_delta is not None and max_delta <= 0.0:
             raise ValueError("max_delta must be positive.")
         if max_delta is not None and max_delta < min_delta:
@@ -834,6 +843,9 @@ def __init__(
         self._target_ess_ratio = target_ess_ratio
         self._max_beta = max_beta
         self._min_delta = min_delta
+        self._beta_tolerance = (
+            min_delta if beta_tolerance is None else beta_tolerance
+        )
         self._max_delta = max_delta
         self._max_bisection_iter = max_bisection_iter
         self._criterion = criterion
@@ -1126,7 +1138,9 @@ def _find_delta(
             low,
             high,
             target_ess_ratio,
-            tolerance=min_delta,
+            tolerance=asarray(
+                self._beta_tolerance, xp=xp, like=base_log_weights
+            ),
             max_iterations=self._max_bisection_iter,
         )
 
diff --git a/tests/test_functional_smc.py b/tests/test_functional_smc.py
index f316f77..a01d4ef 100644
--- a/tests/test_functional_smc.py
+++ b/tests/test_functional_smc.py
@@ -788,6 +788,7 @@ def test_adaptive_tempering_functional_step_can_be_jitted(
         target_ess_ratio=0.8,
         max_beta=0.6,
         min_delta=1e-6,
+        beta_tolerance=1e-8,
         criterion=criterion,
     )
     state = ParticleState(jnp.zeros((4, 1)))
diff --git a/tests/test_prebuilt_samplers.py b/tests/test_prebuilt_samplers.py
index 994b20e..8762655 100644
--- a/tests/test_prebuilt_samplers.py
+++ b/tests/test_prebuilt_samplers.py
@@ -57,6 +57,29 @@ def test_make_standard_bayesian_smc_builds_default_steps() -> None:
     assert isinstance(steps[3], LoggingStep)
 
 
+def test_standard_smc_accepts_independent_beta_tolerance(
+    rng: RandomGenerator,
+) -> None:
+    smc, _, metadata = make_standard_bayesian_smc(
+        lambda x: np.zeros(x.shape[0]),
+        lambda x: x[:, 0] * np.log(4.0),
+        target_ess_ratio=49 / 74,
+        min_delta=0.1,
+        weighting_kwargs={"beta_tolerance": 1e-12, "max_bisection_iter": 60},
+        mutation="none",
+    )
+    state = ParticleState(
+        np.array([[0.0], [1.0]]), log_weights=np.log([0.25, 0.75])
+    )
+    result = smc.run(state, num_steps=1, rng=rng, metadata=metadata)
+    assert float(result.context.metadata["beta"]) == pytest.approx(
+        0.5, abs=1e-11
+    )
+    assert result.final_state.log_evidence == pytest.approx(
+        np.log(7 / 4), abs=1e-11
+    )
+
+
 def test_make_standard_bayesian_smc_reaches_max_beta(rng) -> None:
     max_beta = 0.5
     smc, _, metadata = make_standard_bayesian_smc(
diff --git a/tests/test_steps/test_steps.py b/tests/test_steps/test_steps.py
index 926d0ed..df3cbd2 100644
--- a/tests/test_steps/test_steps.py
+++ b/tests/test_steps/test_steps.py
@@ -564,7 +564,8 @@ def test_adaptive_tempering_solves_known_two_particle_target(
         lambda x: np.array([0.0, np.log(4.0)]),
         criterion=criterion,
         target_ess_ratio=target_ratio,
-        min_delta=1e-10,
+        min_delta=0.1,
+        beta_tolerance=1e-10,
         max_bisection_iter=60,
     )
 
@@ -578,6 +579,41 @@ def test_adaptive_tempering_solves_known_two_particle_target(
     assert not context.stop_requested
 
 
+@pytest.mark.parametrize("tolerance", [0.0, -1.0, np.nan, np.inf, -np.inf])
+def test_adaptive_tempering_rejects_invalid_beta_tolerance(
+    tolerance: float,
+) -> None:
+    with pytest.raises(
+        ValueError, match="beta_tolerance.*finite and positive"
+    ):
+        AdaptiveTemperedWeighting(lambda x: x[:, 0], beta_tolerance=tolerance)
+
+
+@pytest.mark.parametrize("min_delta", [0.1, 0.7])
+def test_beta_tolerance_preserves_minimum_increment_and_default(
+    min_delta: float, rng: RandomGenerator
+) -> None:
+    state = ParticleState(
+        np.array([[0.0], [1.0]]), log_weights=np.log([0.25, 0.75])
+    )
+
+    def run(tolerance: float | None) -> float:
+        step = AdaptiveTemperedWeighting(
+            lambda x: np.array([0.0, np.log(4.0)]),
+            target_ess_ratio=49 / 74,
+            min_delta=min_delta,
+            beta_tolerance=tolerance,
+            max_bisection_iter=60,
+        )
+        _, _, output = step(state, StepContext(t=0), rng)
+        return float(output["delta_beta"])
+
+    assert run(None) == run(min_delta)
+    assert run(1e-12) == pytest.approx(max(0.5, min_delta), abs=1e-11)
+    if min_delta == 0.1:
+        assert abs(run(None) - 0.5) == pytest.approx(0.03125)
+
+
 def test_adaptive_endpoint_skips_bisection(monkeypatch) -> None:
     step = AdaptiveTemperedWeighting(lambda _: np.zeros(4), min_delta=1e-8)
     calls = 0