diff --git a/activeft/sift.py b/activeft/sift.py
index 22758d7..a76806b 100644
--- a/activeft/sift.py
+++ b/activeft/sift.py
@@ -56,6 +56,7 @@ def __init__(
         lambda_: float = 0.01,
         fast: bool = False,
         also_query_opposite: bool = True,
+        alpha: float | None = None,
         only_faiss: bool = False,
         device: torch.device | None = None,
     ):
@@ -65,11 +66,13 @@ def __init__(
         :param lambda_: Value of the lambda parameter of SIFT. Ignored if `acquisition_function` is set.
         :param fast: Whether to use the SIFT-Fast. Ignored if `acquisition_function` is set.
         :param also_query_opposite: If using an inner product index, setting this to `True` will also query the opposite of the query embeddings, pre-selecting points with high *absolute* inner product.
+        :param alpha: Adaptive stopping criterion. Does not apply stopping criterion if set to `None`.
         :param only_faiss: Whether to only use Faiss for search.
         :param device: Device to use for computation.
         """
         self.index = index
         self.also_query_opposite = also_query_opposite
+        self.alpha = alpha
         self.only_faiss = only_faiss
         self.device = (
             device
@@ -100,6 +103,11 @@ def __init__(
                 noise_std=np.sqrt(lambda_),
             )
 
+        if self.alpha is not None:
+            assert isinstance(self.acquisition_function, LazyVTL) or isinstance(
+                self.acquisition_function, VTL
+            ), "Adaptive SIFT can only be used with VTL acquisition function."
+
     def search(
         self,
         query: np.ndarray,
@@ -189,11 +197,22 @@ def engine(i: int) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
                 acquisition_function=self.acquisition_function,
                 device=self.device,
             ).next()
-            return (
-                np.array(values),
-                np.array(I[i][sub_indexes]),
-                np.array(V[i][sub_indexes]),
-            )
+            values = np.array(values)
+            indices = np.array(I[i][sub_indexes])
+            embeddings = np.array(V[i][sub_indexes])
+
+            # Adaptive SIFT
+            if self.alpha is not None:
+                uncertainty = np.sqrt(-values)
+                iteration = np.arange(uncertainty.shape[0]) + 1
+                stopped = uncertainty > 1 / (self.alpha * iteration)
+                values, indices, embeddings = (
+                    values[~stopped],
+                    indices[~stopped],
+                    embeddings[~stopped],
+                )
+
+            return values, indices, embeddings
 
         t_start = time.time()
         resulting_values = []
@@ -210,9 +229,12 @@ def engine(i: int) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
                 resulting_embeddings.append(embeddings)
         t_sift = time.time() - t_start
         retrieval_time = RetrievalTime(faiss=t_faiss, sift=t_sift)
+        dtype = (
+            None if self.alpha is None else object
+        )  # Array of adaptive SIFT might have inconsistent lengths
         return (
-            np.array(resulting_values),
-            np.array(resulting_indices),
-            np.array(resulting_embeddings),
+            np.array(resulting_values, dtype=dtype),
+            np.array(resulting_indices, dtype=dtype),
+            np.array(resulting_embeddings, dtype=dtype),
             retrieval_time,
         )