diff --git a/src/tranquilo/options.py b/src/tranquilo/options.py
index 17b9478..c83eced 100644
--- a/src/tranquilo/options.py
+++ b/src/tranquilo/options.py
@@ -39,11 +39,17 @@ def get_default_acceptance_decider(noisy):
     return "noisy" if noisy else "classic"
 
 
-def get_default_sample_size(model_type, x):
+def get_default_sample_size(model_type, x, noisy, batch_size):
     if model_type == "quadratic":
         out = 2 * len(x) + 1
     else:
-        out = len(x) + 1
+        # Use one point more for the standard least-squares case. Benchmarks have not
+        # shown an improved performance for the noisy or parallel case with one
+        # additional point.
+        if noisy or batch_size > 1:
+            out = len(x) + 1
+        else:
+            out = len(x) + 2
 
     return out
 
diff --git a/src/tranquilo/process_arguments.py b/src/tranquilo/process_arguments.py
index 4bb9821..579fd65 100644
--- a/src/tranquilo/process_arguments.py
+++ b/src/tranquilo/process_arguments.py
@@ -165,6 +165,8 @@ def process_arguments(
         sample_size=sample_size,
         model_type=model_type,
         x=x,
+        noisy=noisy,
+        batch_size=batch_size,
     )
     model_fitter = _process_model_fitter(
         model_fitter, model_type=model_type, sample_size=target_sample_size, x=x
@@ -285,9 +287,11 @@ def _process_sample_filter(sample_filter, batch_size):
     return out
 
 
-def _process_sample_size(sample_size, model_type, x):
+def _process_sample_size(sample_size, model_type, x, noisy, batch_size):
     if sample_size is None:
-        out = get_default_sample_size(model_type=model_type, x=x)
+        out = get_default_sample_size(
+            model_type=model_type, x=x, noisy=noisy, batch_size=batch_size
+        )
     elif callable(sample_size):
         out = sample_size(x=x, model_type=model_type)
     else:
diff --git a/tests/test_process_arguments.py b/tests/test_process_arguments.py
index 4e4af10..7841593 100644
--- a/tests/test_process_arguments.py
+++ b/tests/test_process_arguments.py
@@ -41,15 +41,42 @@ def test_process_batch_size_invalid():
 
 def test_process_sample_size():
     x = np.arange(3)
-    assert _process_sample_size(sample_size=None, model_type="linear", x=x) == 4
-    assert _process_sample_size(sample_size=None, model_type="quadratic", x=x) == 7
-    assert _process_sample_size(10, None, None) == 10
+    assert (
+        _process_sample_size(
+            sample_size=None, model_type="linear", x=x, noisy=True, batch_size=1
+        )
+        == 4
+    )
+    assert (
+        _process_sample_size(
+            sample_size=None, model_type="linear", x=x, noisy=False, batch_size=2
+        )
+        == 4
+    )
+    assert (
+        _process_sample_size(
+            sample_size=None, model_type="linear", x=x, noisy=False, batch_size=1
+        )
+        == 5
+    )
+    assert (
+        _process_sample_size(
+            sample_size=None, model_type="quadratic", x=x, noisy=False, batch_size=1
+        )
+        == 7
+    )
+    assert _process_sample_size(10, None, None, False, 1) == 10
 
 
 def test_process_sample_size_callable():
     x = np.arange(3)
     sample_size = lambda x, model_type: len(x) ** 2
-    assert _process_sample_size(sample_size=sample_size, model_type="linear", x=x) == 9
+    assert (
+        _process_sample_size(
+            sample_size=sample_size, model_type="linear", x=x, noisy=False, batch_size=1
+        )
+        == 9
+    )
 
 
 def test_process_model_type():