diff --git a/src/user/user_mesh.cc b/src/user/user_mesh.cc
index e0d6f938..8d99c79f 100644
--- a/src/user/user_mesh.cc
+++ b/src/user/user_mesh.cc
@@ -1014,8 +1014,8 @@ void mjCMesh::Process(void) {
   mju_eig3(eigval, eigvec, quattmp, full);
 
   // check eigval - SHOULD NOT OCCUR
-  if (eigval[2]<mjEPS) {
-    throw mjCError(this, "eigenvalue of mesh inertia too small: %s", name.c_str());
+  if (eigval[2]<=0) {
+    throw mjCError(this, "eigenvalue of mesh inertia must be positive: %s", name.c_str());
   }
   if (eigval[0] + eigval[1] < eigval[2] ||
       eigval[0] + eigval[2] < eigval[1] ||
diff --git a/src/user/user_model.cc b/src/user/user_model.cc
index 03f544b1..d43a4e06 100644
--- a/src/user/user_model.cc
+++ b/src/user/user_model.cc
@@ -2494,7 +2494,7 @@ mjModel* mjCModel::Compile(const mjVFS* vfs) {
 
         // error
         if (!ok) {
-          throw mjCError(b, "mass and inertia of moving bodies must be positive");
+          throw mjCError(b, "mass and inertia of moving bodies must be larger than mjMINVAL");
         }
       }
     }
diff --git a/test/user/user_mesh_test.cc b/test/user/user_mesh_test.cc
index af5c2c5a..41435841 100644
--- a/test/user/user_mesh_test.cc
+++ b/test/user/user_mesh_test.cc
@@ -31,8 +31,6 @@ namespace {
 
 using MjCMeshTest = MujocoTest;
 
-// yuval: why do we want these anyway? why not string literals in the tests?
-// this does not improve readabillity IMO.
 static const char* const kDuplicateVerticesPath =
     "user/testdata/duplicate_vertices.xml";
 static const char* const kCubePath =
@@ -46,6 +44,8 @@ static const char* const kTexturedTorusPath =
 static const char* const kDuplicateOBJPath =
     "user/testdata/duplicate.xml";
 
+using ::testing::HasSubstr;
+
 // ------------- test vertex de-duplication (STL) ------------------------------
 
 TEST_F(MjCMeshTest, DeDuplicateSTLVertices) {
@@ -116,5 +116,63 @@ TEST_F(MjCMeshTest, SaveMeshOnce) {
   mj_deleteModel(model);
 }
 
+TEST_F(MujocoTest, TinyMeshLoads) {
+  static constexpr char xml[] = R"(
+  <mujoco>
+    <asset>
+      <mesh name="tiny" vertex="0 0 0  1e-4 0 0  0 1e-4 0  0 0 1e-4"/>
+    </asset>
+    <worldbody>
+      <geom type="mesh" mesh="tiny"/>
+    </worldbody>
+  </mujoco>
+  )";
+  mjModel* model = LoadModelFromString(xml, 0, 0);
+  ASSERT_THAT(model, testing::NotNull());
+  mj_deleteModel(model);
+}
+
+TEST_F(MujocoTest, SmallInertiaLoads) {
+  static constexpr char xml[] = R"(
+  <mujoco>
+    <asset>
+      <mesh name="tiny" vertex="0 0 0  1e-4 0 0  0 1e-4 0  0 0 1e-4"/>
+    </asset>
+    <worldbody>
+      <body>
+        <freejoint/>
+        <geom type="mesh" mesh="tiny"/>
+        <geom name="small" size=".001"/>
+      </body>
+    </worldbody>
+  </mujoco>
+  )";
+  mjModel* model = LoadModelFromString(xml, 0, 0);
+  ASSERT_THAT(model, testing::NotNull());
+  mj_deleteModel(model);
+}
+
+TEST_F(MujocoTest, TinyInertiaFails) {
+  static constexpr char xml[] = R"(
+  <mujoco>
+    <asset>
+      <mesh name="tiny" vertex="0 0 0  1e-4 0 0  0 1e-4 0  0 0 1e-4"/>
+    </asset>
+    <worldbody>
+      <body>
+        <freejoint/>
+        <geom type="mesh" mesh="tiny"/>
+      </body>
+    </worldbody>
+  </mujoco>
+  )";
+  std::array<char, 1024> error;
+  LoadModelFromString(xml, error.data(), error.size());
+  EXPECT_THAT(
+      error.data(),
+      HasSubstr(
+          "mass and inertia of moving bodies must be larger than mjMINVAL"));
+}
+
 }  // namespace
 }  // namespace mujoco