@@ -261,17 +261,15 @@ class Learner1D(BaseLearner):

             return [], []

         # If the bounds have not been chosen yet, we choose them first.

-        points = [b for b in self.bounds if b not in self.data

-                  and b not in self.pending_points]

+        missing_bounds = [b for b in self.bounds if b not in self.data

+                          and b not in self.pending_points]

-        if len(points) == 2:

-            # First time

+        if missing_bounds:

             loss_improvements = [np.inf] * n

-            points = np.linspace(*self.bounds, n).tolist()

-        elif len(points) == 1:

-            # Second time, if we previously returned just self.bounds[0]

-            loss_improvements = [np.inf] * n

-            points = np.linspace(*self.bounds, n + 1)[1:].tolist()

+            # XXX: should check if points are present in self.data or self.pending_points

+            points = np.linspace(*self.bounds, n + 2 - len(missing_bounds)).tolist()

+            if len(missing_bounds) == 1:

+                points = points[1:] if missing_bounds[0] == self.bounds[1] else points[:-1]

         else:

             def xs(x_left, x_right, n):

                 if n == 1:

@@ -363,7 +363,7 @@ def test_learner1d_first_iteration():

     """Edge cases where we ask for a few points at the start."""

     learner = Learner1D(lambda x: None, (-1, 1))

     points, loss_improvements = learner.ask(2)

-    assert set(points) == set([-1, 1])

+    assert set(points) == set(learner.bounds)

     learner = Learner1D(lambda x: None, (-1, 1))

     points, loss_improvements = learner.ask(3)

@@ -371,17 +371,27 @@ def test_learner1d_first_iteration():

     learner = Learner1D(lambda x: None, (-1, 1))

     points, loss_improvements = learner.ask(1)

-    assert len(points) == 1 and points[0] in [-1, 1]

+    assert len(points) == 1 and points[0] in learner.bounds

     rest = set([-1, 0, 1]) - set(points)

     points, loss_improvements = learner.ask(2)

     assert set(points) == set(rest)

     learner = Learner1D(lambda x: None, (-1, 1))

     points, loss_improvements = learner.ask(1)

-    to_see = set([-1, 1]) - set(points)

+    to_see = set(learner.bounds) - set(points)

     points, loss_improvements = learner.ask(1)

     assert set(points) == set(to_see)

+    learner = Learner1D(lambda x: None, (-1, 1))

+    learner.tell(1, 0)

+    points, loss_improvements = learner.ask(1)

+    assert points == [-1]

+

+    learner = Learner1D(lambda x: None, (-1, 1))

+    learner.tell(-1, 0)

+    points, loss_improvements = learner.ask(1)

+    assert points == [1]

+

 def _run_on_discontinuity(x_0, bounds):