diff --git a/Lib/fontTools/varLib/instancer/solver.py b/Lib/fontTools/varLib/instancer/solver.py
index 665def6fe..b3746c374 100644
--- a/Lib/fontTools/varLib/instancer/solver.py
+++ b/Lib/fontTools/varLib/instancer/solver.py
@@ -4,6 +4,8 @@ from functools import lru_cache
 
 __all__ = ['rebaseTent']
 
+EPSILON = 1 / (1 << 14)
+
 def _reverse_negate(v):
     return (-v[2], -v[1], -v[0])
 
@@ -130,6 +132,10 @@ def _solve(tent, axisLimit, negative=False):
         #                           |
         #                      crossing
         else:
+            # A tent's peak cannot fall on axis default. Nudge it.
+            if upper == axisDef:
+                upper += EPSILON
+
             # Downslope.
             loc1 = (crossing, upper, axisMax)
             scalar1 = 0
@@ -241,6 +247,10 @@ def _solve(tent, axisLimit, negative=False):
     #                    axisDef
     #
     else:
+        # A tent's peak cannot fall on axis default. Nudge it.
+        if lower == axisDef:
+            lower -= EPSILON
+
         # Downslope.
         loc1 = (axisMin, lower, axisDef)
         scalar1 = 0
@@ -252,27 +262,7 @@ def _solve(tent, axisLimit, negative=False):
         out.append((scalar1 - gain, loc1))
         out.append((scalar2 - gain, loc2))
 
-
-    # If peak ended up being zero, nudge it to the next value
-    EPSILON = 1 / (1 << 14)
-    new_out = []
-    for scalar,triple in out:
-        if scalar == 0:
-            continue
-
-        if triple is None:
-            new_out.append((scalar, triple))
-            continue
-
-        lower,peak,upper = triple
-        if peak == axisDef:
-            assert not (lower == upper == axisDef)
-
-            peak += EPSILON if lower == axisDef else -EPSILON
-
-        new_out.append((scalar, (lower,peak,upper)))
-
-    return new_out
+    return out
 
 
 @lru_cache(128)
@@ -299,6 +289,6 @@ def rebaseTent(tent, axisLimit):
     sols = _solve(tent, axisLimit)
 
     n = lambda v: normalizeValue(v, axisLimit, extrapolate=True)
-    sols = [(scalar, (n(v[0]), n(v[1]), n(v[2])) if v is not None else None) for scalar,v in sols]
+    sols = [(scalar, (n(v[0]), n(v[1]), n(v[2])) if v is not None else None) for scalar,v in sols if scalar]
 
     return sols
diff --git a/Tests/varLib/instancer/solver_test.py b/Tests/varLib/instancer/solver_test.py
index c64c8764a..606f58712 100644
--- a/Tests/varLib/instancer/solver_test.py
+++ b/Tests/varLib/instancer/solver_test.py
@@ -219,9 +219,9 @@ class RebaseTentTest(object):
                 [
                     (1, None),
                     (-1, (0, 0.0001220703, 1)),
-                    (-1, (0, 1, 1)),
+                    (-1, (0.0001220703, 1, 1)),
                     (-1, (-1, -0.0001220703, 0)),
-                    (-1, (-1, -1, 0)),
+                    (-1, (-1, -1, -0.0001220703)),
                 ]
             ),
         ],