diff --git a/klippy/toolhead.py b/klippy/toolhead.py
index 4149d53b12f6..f90f5dd0289c 100644
--- a/klippy/toolhead.py
+++ b/klippy/toolhead.py
@@ -64,32 +64,32 @@ def calc_junction(self, prev_move):
             return
         # Allow extruder to calculate its maximum junction
         extruder_v2 = self.toolhead.extruder.calc_junction(prev_move, self)
+        max_start_v2 = min(
+            extruder_v2, self.max_cruise_v2, prev_move.max_cruise_v2,
+            prev_move.max_start_v2 + prev_move.delta_v2)
         # Find max velocity using "approximated centripetal velocity"
         axes_r = self.axes_r
         prev_axes_r = prev_move.axes_r
         junction_cos_theta = -(axes_r[0] * prev_axes_r[0]
                                + axes_r[1] * prev_axes_r[1]
                                + axes_r[2] * prev_axes_r[2])
-        if junction_cos_theta > 0.999999:
-            return
-        junction_cos_theta = max(junction_cos_theta, -0.999999)
-        sin_theta_d2 = math.sqrt(0.5*(1.0-junction_cos_theta))
-        R_jd = sin_theta_d2 / (1. - sin_theta_d2)
-        # Approximated circle must contact moves no further away than mid-move
-        tan_theta_d2 = sin_theta_d2 / math.sqrt(0.5*(1.0+junction_cos_theta))
-        move_centripetal_v2 = .5 * self.move_d * tan_theta_d2 * self.accel
-        prev_move_centripetal_v2 = (.5 * prev_move.move_d * tan_theta_d2
-                                    * prev_move.accel)
+        sin_theta_d2 = math.sqrt(max(0.5*(1.0-junction_cos_theta), 0.))
+        cos_theta_d2 = math.sqrt(max(0.5*(1.0+junction_cos_theta), 0.))
+        one_minus_sin_theta_d2 = 1. - sin_theta_d2
+        if one_minus_sin_theta_d2 > 0. and cos_theta_d2 > 0.:
+            R_jd = sin_theta_d2 / one_minus_sin_theta_d2
+            move_jd_v2 = R_jd * self.junction_deviation * self.accel
+            pmove_jd_v2 = R_jd * prev_move.junction_deviation * prev_move.accel
+            # Approximated circle must contact moves no further than mid-move
+            quarter_tan_theta_d2 = .25 * sin_theta_d2 / cos_theta_d2
+            move_centripetal_v2 = quarter_tan_theta_d2 * self.delta_v2
+            pmove_centripetal_v2 = quarter_tan_theta_d2 * prev_move.delta_v2
+            max_start_v2 = min(max_start_v2, move_jd_v2, pmove_jd_v2,
+                               move_centripetal_v2, pmove_centripetal_v2)
         # Apply limits
-        self.max_start_v2 = min(
-            R_jd * self.junction_deviation * self.accel,
-            R_jd * prev_move.junction_deviation * prev_move.accel,
-            move_centripetal_v2, prev_move_centripetal_v2,
-            extruder_v2, self.max_cruise_v2, prev_move.max_cruise_v2,
-            prev_move.max_start_v2 + prev_move.delta_v2)
+        self.max_start_v2 = max_start_v2
         self.max_smoothed_v2 = min(
-            self.max_start_v2
-            , prev_move.max_smoothed_v2 + prev_move.smooth_delta_v2)
+            max_start_v2, prev_move.max_smoothed_v2 + prev_move.smooth_delta_v2)
     def set_junction(self, start_v2, cruise_v2, end_v2):
         # Determine accel, cruise, and decel portions of the move distance
         half_inv_accel = .5 / self.accel