diff --git a/plugins/printers/services/supply_history.py b/plugins/printers/services/supply_history.py
index e3e6bda..9f3b16f 100644
--- a/plugins/printers/services/supply_history.py
+++ b/plugins/printers/services/supply_history.py
@@ -37,6 +37,18 @@ NEW_CARTRIDGE_LEVEL = 80
 # through a coarse gauge can "prove" any rate at all.
 MIN_POINTS_FOR_ESTIMATE = 4
 
+# A rate needs TIME behind it, not just readings. Supply items are often polled
+# every few minutes, so four readings can span a quarter of an hour - and a 2
+# point drop across fifteen minutes extrapolates to nearly 200 percent a day,
+# which is how a cartridge sitting at 82 percent gets forecast to run out in a
+# fortnight. The history window can be short for the same reason: the fetch
+# keeps the newest rows up to a per-item cap, so a fast-polled item returns days
+# rather than the ninety asked for.
+#
+# Two days is the smallest span that survives a printer's daily rhythm - a
+# single heavy morning does not become the whole picture.
+MIN_DAYS_FOR_ESTIMATE = 2
+
 # Many printers report in 10% steps, so a fortnight can pass on one plateau.
 # Without a minimum observed drop the slope reads as zero and the forecast
 # says "never", which is worse than saying nothing.
@@ -201,7 +213,7 @@ def burn_rate(points):
     if len(points) < MIN_POINTS_FOR_ESTIMATE:
         return None
     total_days = (points[-1][0] - points[0][0]).total_seconds() / 86400
-    if total_days <= 0:
+    if total_days < MIN_DAYS_FOR_ESTIMATE:
         return None
     # The overall drop still gates the estimate: a gauge sitting on one plateau
     # has not proved anything yet, whatever the intervals say.
@@ -290,7 +302,8 @@ def analyse(points, rise=REPLACEMENT_RISE, currentlevel=None):
 
     if rate is None:
         # Say which of the three it is; "no estimate" alone invites a bug report.
-        if len(run) < MIN_POINTS_FOR_ESTIMATE:
+        basis = result.get('basisdays') or 0
+        if len(run) < MIN_POINTS_FOR_ESTIMATE or basis < MIN_DAYS_FOR_ESTIMATE:
             result['reason'] = ('replaced recently' if replacements
                                 else 'not enough history yet')
         else:
diff --git a/tests/test_plugins/test_supply_history.py b/tests/test_plugins/test_supply_history.py
index 90d17bf..0d8e1ba 100644
--- a/tests/test_plugins/test_supply_history.py
+++ b/tests/test_plugins/test_supply_history.py
@@ -339,3 +339,26 @@ def test_a_real_near_empty_reading_before_a_swap_is_kept():
     points = normalise(series([40, 30, 5, 100, 95, 90]))
     assert 5.0 in [level for _, level in points]
     assert len(find_replacements(points)) == 1
+
+
+def test_minutes_of_readings_do_not_forecast_weeks():
+    """Supply items are often polled every few minutes.
+
+    Four readings a quarter of an hour apart, with a 2 point drop between the
+    ends, used to extrapolate to nearly 200 percent a day - so a cartridge
+    sitting at 82 percent was forecast to run out in a fortnight. A rate needs
+    time behind it, and without it the honest answer is no estimate.
+    """
+    minutes = 5
+    detail = analyse(series([84, 83, 83, 82], hours=minutes / 60))
+    assert detail['burnrateperday'] is None
+    assert detail['daysleft'] is None
+    assert detail['reason'] == 'not enough history yet'
+    assert band(detail['daysleft']) is None      # lands in "No estimate yet"
+
+
+def test_a_run_with_enough_days_still_estimates():
+    """The guard must not silence a genuinely slow, genuinely long run."""
+    detail = analyse(series([84, 83, 82, 81, 80, 79]))
+    assert detail['burnrateperday'] == 1.0
+    assert detail['daysleft'] == 79