diff --git a/skyfield/jpllib.py b/skyfield/jpllib.py
index 13ff0aa9..9fd8bf5d 100644
--- a/skyfield/jpllib.py
+++ b/skyfield/jpllib.py
@@ -261,8 +261,15 @@ def _at(self, t):
             for segment in reversed(self.segments):
                 spk = segment.spk_segment
                 if spk.start_jd <= t.tdb <= spk.end_jd:
-                    break
-            return segment._at(t)
+                    return segment._at(t)
+
+            start_time, _ = self.segments[0].time_range(t.ts)
+            _, end_time = self.segments[-1].time_range(t.ts)
+            text = (
+                'none of the {0} ephemeris segments for target {1} '
+                'cover date {2}'
+            ).format(len(self.segments), self.target, t.utc_iso())
+            raise EphemerisRangeError(text, start_time, end_time, True, None)
 
         shape = (3,) + t.shape
         position = np.empty(shape)
diff --git a/skyfield/tests/test_jpllib.py b/skyfield/tests/test_jpllib.py
index fceaf166..eb9524ce 100644
--- a/skyfield/tests/test_jpllib.py
+++ b/skyfield/tests/test_jpllib.py
@@ -1,11 +1,35 @@
 import os
 from skyfield.api import load, load_file
+from skyfield.errors import EphemerisRangeError
+from skyfield.jpllib import Stack
 
 from assay import assert_raises
 
 def _data_path(filename):
     return os.path.join(os.path.dirname(__file__), 'data', filename)
 
+class _FakeSpkSegment:
+    def __init__(self, start_jd, end_jd):
+        self.start_jd = start_jd
+        self.end_jd = end_jd
+
+class _FakeSegment:
+    center = 0
+    target = 1
+    ephemeris = None
+
+    def __init__(self, start_jd, end_jd):
+        self.spk_segment = _FakeSpkSegment(start_jd, end_jd)
+        self.called = False
+
+    def _at(self, t):
+        self.called = True
+        return None
+
+    def time_range(self, ts):
+        spk = self.spk_segment
+        return ts.tdb_jd(spk.start_jd), ts.tdb_jd(spk.end_jd)
+
 # Test file generated with:
 # python -m jplephem excerpt 1969/07/29 1969/07/30 de441.bsp de441-1969.bsp
 
@@ -30,6 +54,17 @@ def test_multiple_non_overlapping_segments_per_target():
 
     # TODO: SSB.at(t).observe() fails the above test.
 
+def test_stack_scalar_no_matching_segment_raises_without_fallthrough():
+    ts = load.timescale()
+    t = ts.tdb_jd(3.0)
+    segments = [_FakeSegment(0.0, 1.0), _FakeSegment(5.0, 6.0)]
+    stack = Stack(segments)
+
+    with assert_raises(EphemerisRangeError, 'none of the 2 ephemeris segments'):
+        stack._at(t)
+
+    assert not any(segment.called for segment in segments)
+
 # Verify that ephemeris objects let their segments be edited.
 
 def test_removing_segments_from_ephemeris():