diff --git a/tests/kernel-cases/construction/cov-axis-edge-on-a-box-edge/expected.json b/tests/kernel-cases/construction/cov-axis-edge-on-a-box-edge/expected.json
new file mode 100644
index 0000000000..b61cb93491
--- /dev/null
+++ b/tests/kernel-cases/construction/cov-axis-edge-on-a-box-edge/expected.json
@@ -0,0 +1,22 @@
+{
+ "sources": [],
+ "what": "an axis on the straight top-back edge of a box",
+ "source": "analytic",
+ "method": "box 40 x 30 x 20 with a corner at the origin (x 0..40, y 0..30, z 0..20): the edge at y 30, z 20 runs along X: the line through (0,30,20) along X",
+ "construction": {
+  "A": {
+   "axis": {
+    "through": [
+     0,
+     30,
+     20
+    ],
+    "dir": [
+     1,
+     0,
+     0
+    ]
+   }
+  }
+ }
+}
diff --git a/tests/kernel-cases/construction/cov-axis-edge-on-a-box-edge/recipe.json b/tests/kernel-cases/construction/cov-axis-edge-on-a-box-edge/recipe.json
new file mode 100644
index 0000000000..56cc1c75d9
--- /dev/null
+++ b/tests/kernel-cases/construction/cov-axis-edge-on-a-box-edge/recipe.json
@@ -0,0 +1,26 @@
+{
+ "commands": [
+  {
+   "command": "solid.box",
+   "params": {
+    "length": 40,
+    "width": 30,
+    "height": 20,
+    "body_name": "Box"
+   }
+  },
+  {
+   "command": "construct.axis.edge",
+   "params": {
+    "edge": {
+     "edge": [
+      20,
+      30,
+      20
+     ]
+    },
+    "name": "A"
+   }
+  }
+ ]
+}
diff --git a/tests/kernel-cases/construction/cov-axis-edge-refuses-a-circular-edge/expected.json b/tests/kernel-cases/construction/cov-axis-edge-refuses-a-circular-edge/expected.json
new file mode 100644
index 0000000000..24177397ee
--- /dev/null
+++ b/tests/kernel-cases/construction/cov-axis-edge-refuses-a-circular-edge/expected.json
@@ -0,0 +1,8 @@
+{
+ "sources": [],
+ "what": "an axis on a circular edge, which is not straight",
+ "source": "analytic",
+ "method": "cylinder r 5, h 10 on (60,0,0) along +Z: its top edge is a circle, no line: refused",
+ "outcome": "refused",
+ "refusal": "the edge is not straight"
+}
diff --git a/tests/kernel-cases/construction/cov-axis-edge-refuses-a-circular-edge/recipe.json b/tests/kernel-cases/construction/cov-axis-edge-refuses-a-circular-edge/recipe.json
new file mode 100644
index 0000000000..fd4d3c507e
--- /dev/null
+++ b/tests/kernel-cases/construction/cov-axis-edge-refuses-a-circular-edge/recipe.json
@@ -0,0 +1,31 @@
+{
+ "commands": [
+  {
+   "command": "solid.cylinder",
+   "params": {
+    "base": [
+     60,
+     0,
+     0
+    ],
+    "radius": 5,
+    "height": 10,
+    "body_name": "Cyl",
+    "operation": "new"
+   }
+  },
+  {
+   "command": "construct.axis.edge",
+   "params": {
+    "edge": {
+     "edge": [
+      65,
+      0,
+      10
+     ]
+    },
+    "name": "A"
+   }
+  }
+ ]
+}