diff --git a/hypothesis-python/RELEASE.rst b/hypothesis-python/RELEASE.rst
new file mode 100644
index 0000000000..147c24f9d6
--- /dev/null
+++ b/hypothesis-python/RELEASE.rst
@@ -0,0 +1,5 @@
+RELEASE_TYPE: patch
+
+This patch makes unique :func:`~hypothesis.extra.numpy.arrays` much more
+efficient, especially when there are only a few valid elements - such as
+for eight-bit integers (:issue:`3066`).
diff --git a/hypothesis-python/src/hypothesis/extra/numpy.py b/hypothesis-python/src/hypothesis/extra/numpy.py
index 5d83443509..4b09fa2b20 100644
--- a/hypothesis-python/src/hypothesis/extra/numpy.py
+++ b/hypothesis-python/src/hypothesis/extra/numpy.py
@@ -186,9 +186,7 @@ def __init__(self, element_strategy, shape, dtype, fill, unique):
         self.unique = unique
         self._check_elements = dtype.kind not in ("O", "V")
 
-    def set_element(self, data, result, idx, strategy=None):
-        strategy = strategy or self.element_strategy
-        val = data.draw(strategy)
+    def set_element(self, val, result, idx, *, fill=False):
         try:
             result[idx] = val
         except TypeError as err:
@@ -197,6 +195,7 @@ def set_element(self, data, result, idx, strategy=None):
                 f"{result.dtype!r} - possible mismatch of time units in dtypes?"
             ) from err
         if self._check_elements and val != result[idx] and val == val:
+            strategy = self.fill if fill else self.element_strategy
             raise InvalidArgument(
                 "Generated array element %r from %r cannot be represented as "
                 "dtype %r - instead it becomes %r (type %r).  Consider using a more "
@@ -229,28 +228,17 @@ def do_draw(self, data):
             # generate a fully dense array with a freshly drawn value for each
             # entry.
             if self.unique:
-                seen = set()
-                elements = cu.many(
-                    data,
+                elems = st.lists(
+                    self.element_strategy,
                     min_size=self.array_size,
                     max_size=self.array_size,
-                    average_size=self.array_size,
+                    unique=True,
                 )
-                i = 0
-                while elements.more():
-                    # We assign first because this means we check for
-                    # uniqueness after numpy has converted it to the relevant
-                    # type for us. Because we don't increment the counter on
-                    # a duplicate we will overwrite it on the next draw.
-                    self.set_element(data, result, i)
-                    if result[i] not in seen:
-                        seen.add(result[i])
-                        i += 1
-                    else:
-                        elements.reject()
+                for i, v in enumerate(data.draw(elems)):
+                    self.set_element(v, result, i)
             else:
                 for i in range(len(result)):
-                    self.set_element(data, result, i)
+                    self.set_element(data.draw(self.element_strategy), result, i)
         else:
             # We draw numpy arrays as "sparse with an offset". We draw a
             # collection of index assignments within the array and assign
@@ -277,7 +265,7 @@ def do_draw(self, data):
                 if not needs_fill[i]:
                     elements.reject()
                     continue
-                self.set_element(data, result, i)
+                self.set_element(data.draw(self.element_strategy), result, i)
                 if self.unique:
                     if result[i] in seen:
                         elements.reject()
@@ -300,7 +288,7 @@ def do_draw(self, data):
                 one_element = np.zeros(
                     shape=1, dtype=object if unsized_string_dtype else self.dtype
                 )
-                self.set_element(data, one_element, 0, self.fill)
+                self.set_element(data.draw(self.fill), one_element, 0, fill=True)
                 if unsized_string_dtype:
                     one_element = one_element.astype(self.dtype)
                 fill_value = one_element[0]
diff --git a/hypothesis-python/src/hypothesis/strategies/_internal/core.py b/hypothesis-python/src/hypothesis/strategies/_internal/core.py
index a446874918..4cc8f3941d 100644
--- a/hypothesis-python/src/hypothesis/strategies/_internal/core.py
+++ b/hypothesis-python/src/hypothesis/strategies/_internal/core.py
@@ -95,7 +95,12 @@
 from hypothesis.strategies._internal.functions import FunctionStrategy
 from hypothesis.strategies._internal.lazy import LazyStrategy
 from hypothesis.strategies._internal.misc import just, none, nothing
-from hypothesis.strategies._internal.numbers import Real, floats, integers
+from hypothesis.strategies._internal.numbers import (
+    IntegersStrategy,
+    Real,
+    floats,
+    integers,
+)
 from hypothesis.strategies._internal.recursive import RecursiveStrategy
 from hypothesis.strategies._internal.shared import SharedStrategy
 from hypothesis.strategies._internal.strategies import (
@@ -283,6 +288,20 @@ def lists(
             tuple_suffixes = TupleStrategy(elements.element_strategies[1:])
             elements = elements.element_strategies[0]
 
+        # UniqueSampledListStrategy offers a substantial performance improvement for
+        # unique arrays with few possible elements, e.g. of eight-bit integer types.
+        if (
+            isinstance(elements, IntegersStrategy)
+            and None not in (elements.start, elements.end)
+            and (elements.end - elements.start) <= 255
+        ):
+            elements = SampledFromStrategy(
+                sorted(range(elements.start, elements.end + 1), key=abs)
+                if elements.end < 0 or elements.start > 0
+                else list(range(0, elements.end + 1))
+                + list(range(-1, elements.start - 1, -1))
+            )
+
         if isinstance(elements, SampledFromStrategy):
             element_count = len(elements.elements)
             if min_size > element_count:
diff --git a/hypothesis-python/tests/numpy/test_gen_data.py b/hypothesis-python/tests/numpy/test_gen_data.py
index b3d95a6484..640562d189 100644
--- a/hypothesis-python/tests/numpy/test_gen_data.py
+++ b/hypothesis-python/tests/numpy/test_gen_data.py
@@ -21,7 +21,7 @@
 import pytest
 
 from hypothesis import HealthCheck, assume, given, note, settings, strategies as st
-from hypothesis.errors import InvalidArgument, Unsatisfiable
+from hypothesis.errors import InvalidArgument
 from hypothesis.extra import numpy as nps
 
 from tests.common.debug import find_any, minimal
@@ -251,7 +251,7 @@ def test_array_values_are_unique(arr):
 
 def test_cannot_generate_unique_array_of_too_many_elements():
     strat = nps.arrays(dtype=int, elements=st.integers(0, 5), shape=10, unique=True)
-    with pytest.raises(Unsatisfiable):
+    with pytest.raises(InvalidArgument):
         strat.example()
 
 
@@ -274,6 +274,23 @@ def test_generates_all_values_for_unique_array(arr):
     assert len(set(arr)) == len(arr)
 
 
+@given(nps.arrays(dtype="int8", shape=255, unique=True))
+def test_efficiently_generates_all_unique_array(arr):
+    # Avoids the birthday paradox with UniqueSampledListStrategy
+    assert len(set(arr)) == len(arr)
+
+
+@given(st.data(), st.integers(-100, 100), st.integers(1, 100))
+def test_array_element_rewriting(data, start, size):
+    arr = nps.arrays(
+        dtype=np.dtype("int64"),
+        shape=size,
+        elements=st.integers(start, start + size - 1),
+        unique=True,
+    )
+    assert set(data.draw(arr)) == set(range(start, start + size))
+
+
 def test_may_fill_with_nan_when_unique_is_set():
     find_any(
         nps.arrays(