diff --git a/src/Magnum/Math/DualQuaternion.h b/src/Magnum/Math/DualQuaternion.h
index 58b10a672..7eed6bf8a 100644
--- a/src/Magnum/Math/DualQuaternion.h
+++ b/src/Magnum/Math/DualQuaternion.h
@@ -34,6 +34,7 @@
 #include "Magnum/Math/Dual.h"
 #include "Magnum/Math/Matrix4.h"
 #include "Magnum/Math/Quaternion.h"
+#include "Magnum/Math/Functions.h"
 
 namespace Magnum { namespace Math {
 
@@ -67,6 +68,12 @@ template<class T> inline DualQuaternion<T> sclerp(const DualQuaternion<T>& norma
         "Math::sclerp(): dual quaternions must be normalized", {});
     const T dotResult = dot(normalizedA.real().vector(), normalizedB.real().vector());
 
+    /* Avoid division by zero */
+    const T cosHalfAngle = dotResult + normalizedA.real().scalar()*normalizedB.real().scalar();
+    if(std::abs(cosHalfAngle) >= T(1)) {
+        return DualQuaternion<T>{normalizedA.real(), Quaternion<T>{Math::lerp(normalizedA.dual().vector(), normalizedB.dual().vector(), t), T(0)}};
+    }
+
     /* l + εm = q_A^**q_B, multiplying with -1 ensures shortest path when dot < 0 */
     const DualQuaternion<T> diff = normalizedA.quaternionConjugated()*(dotResult < T(0) ? -normalizedB : normalizedB);
     const Quaternion<T>& l = diff.real();
diff --git a/src/Magnum/Math/Test/DualQuaternionTest.cpp b/src/Magnum/Math/Test/DualQuaternionTest.cpp
index cc1cfc7f7..b84d8a3ab 100644
--- a/src/Magnum/Math/Test/DualQuaternionTest.cpp
+++ b/src/Magnum/Math/Test/DualQuaternionTest.cpp
@@ -433,6 +433,17 @@ void DualQuaternionTest::sclerp() {
     CORRADE_COMPARE(interp1, expected1);
     CORRADE_COMPARE(interp2, expected2);
     CORRADE_COMPARE(interp3, expected3);
+
+    /* Edge cases: */
+
+    /* Dual quaternions with identical rotation */
+    CORRADE_COMPARE(Math::sclerp(from, from, 0.42f), from);
+    CORRADE_COMPARE(Math::sclerp(from, DualQuaternion(-from.real(), from.dual()), 0.42f), from);
+
+    /* No difference in rotation, but in translation */
+    const auto rotation = DualQuaternion::rotation(35.0_degf, Vector3{0.3f, 0.2f, 0.1f});
+    CORRADE_COMPARE(Math::sclerp(DualQuaternion::translation(Vector3{1.0f, 2.0f, 4.0f})*rotation, DualQuaternion::translation(Vector3{5, -6, 2})*rotation, 0.25f),
+                    DualQuaternion::translation(Vector3{2.0f, 0.0f, 3.5f})*rotation);
 }
 
 }}}