diff --git a/src/lol/math/transform.h b/src/lol/math/transform.h
index 2d2fd32b..bf951f63 100644
--- a/src/lol/math/transform.h
+++ b/src/lol/math/transform.h
@@ -197,6 +197,7 @@ struct quat_t : public linear_ops::base<T>
         return quat_t(w, -x, -y, -z);
     }
 
+    /* Transform vectors or points */
     inline vec_t<T,3> transform(vec_t<T,3> const &v) const
     {
         quat_t p = quat_t(0, v.x, v.y, v.z);
@@ -268,11 +269,21 @@ struct sqt_t
       : q(other.q), t(other.t), s(other.s) {}
 
     /* Various explicit constructors */
-    inline constexpr sqt_t(T const &s_,
-                           quat_t<T> const &q_,
-                           vec_t<T,3> const &t_)
-      : s(s_), q(q_), t(t_) {}
+    explicit inline constexpr sqt_t(T const &s_,
+                                    quat_t<T> const &q_,
+                                    vec_t<T,3> const &t_)
+      : q(q_), t(t_), s(s_) {}
 
+    explicit inline constexpr sqt_t(T const &s_)
+      : q(1.f), t(0.f), s(s_) {}
+
+    explicit inline constexpr sqt_t(quat_t<T> const &q_)
+      : q(q_), t(0.f), s(1.f) {}
+
+    explicit inline constexpr sqt_t(vec_t<T,3> const &t_)
+      : q(1.f), t(t_), s(1.f) {}
+
+    /* Transform vectors or points */
     inline vec_t<T,3> transform(vec_t<T,3> const &v) const
     {
         return t + q.transform(s * v);
@@ -280,7 +291,7 @@ struct sqt_t
 
     inline vec_t<T,4> transform(vec_t<T,4> const &v) const
     {
-        // XXX: needs serious testing
+        // XXX: needs serious testing for w != 1
         vec_t<T,4> tmp = q.transform(vec_t<T,4>(s * v.xyz, v.w));
         return vec_t<T,4>(tmp.xyz, 0.f) + vec_t<T,4>(t, 1.f) * tmp.w;
     }
@@ -295,6 +306,14 @@ struct sqt_t
         return transform(v);
     }
 
+    /* Compose two SQTs together */
+    inline sqt_t<T> operator *(sqt_t<T> const &other) const
+    {
+        return sqt_t<T>(s * other.s,
+                        q * other.q,
+                        transform(other.t));
+    }
+
     quat_t<T> q;
     vec_t<T,3> t;
     T s;
diff --git a/src/t/math/sqt.cpp b/src/t/math/sqt.cpp
new file mode 100644
index 00000000..5bdff20c
--- /dev/null
+++ b/src/t/math/sqt.cpp
@@ -0,0 +1,94 @@
+//
+//  Lol Engine — Unit tests for the SQT transform class
+//
+//  Copyright © 2010—2015 Sam Hocevar <sam@hocevar.net>
+//
+//  Lol Engine is free software. It comes without any warranty, to
+//  the extent permitted by applicable law. You can redistribute it
+//  and/or modify it under the terms of the Do What the Fuck You Want
+//  to Public License, Version 2, as published by the WTFPL Task Force.
+//  See http://www.wtfpl.net/ for more details.
+//
+
+#include <lol/engine-internal.h>
+
+#include <lolunit.h>
+
+namespace lol
+{
+
+static sqt const test_sqt_1(1.5f,
+                            quat::rotate(radians(20.f),
+                                         normalize(vec3(1.f, 2.f, 3.f))),
+                            vec3(1.f, -1.f, 0.5f));
+
+static vec4 test_vec4s[] =
+{
+    vec4(1.f, 0.f, 0.f, 1.f),
+    vec4(0.f, 1.f, 0.f, 1.f),
+    vec4(0.f, 0.f, 1.f, 1.f),
+    vec4(1.f, 2.f, 3.f, 1.f),
+    vec4(-1.f, 50.f, 12.f, 1.f),
+    vec4(20.f, -10.f, 0.f, 1.f),
+    vec4(-20.f, 10.f, 8.f, 1.f),
+};
+
+lolunit_declare_fixture(sqt_test)
+{
+    lolunit_declare_test(transform_vec3_vec4)
+    {
+        /* We check that transforming a vec3 and a vec4 with w==1
+         * yield the same results. */
+        for (vec4 v0 : test_vec4s)
+        {
+            vec4 v1 = test_sqt_1.transform(v0);
+            vec3 v2 = test_sqt_1.transform(v0.xyz);
+
+            lolunit_assert_doubles_equal(v1.x, v2.x, 1e-5f);
+            lolunit_assert_doubles_equal(v1.y, v2.y, 1e-5f);
+            lolunit_assert_doubles_equal(v1.z, v2.z, 1e-5f);
+            lolunit_assert_doubles_equal(v1.w, 1.0f, 1e-5f);
+        }
+    }
+
+    lolunit_declare_test(sqt_vs_matrix_vec4)
+    {
+        /* We check that transforming a vec4 with an SQT and a
+         * vec4 with a product of 4×4 matrices yield the same
+         * results. */
+        mat4 m = mat4::translate(test_sqt_1.t)
+               * mat4(test_sqt_1.q)
+               * mat4::scale(test_sqt_1.s);
+
+        for (vec4 v0 : test_vec4s)
+        {
+            vec4 v1 = test_sqt_1 * v0;
+            vec4 v2 = m * v0;
+
+            lolunit_assert_doubles_equal(v1.x, v2.x, 1e-5f);
+            lolunit_assert_doubles_equal(v1.y, v2.y, 1e-5f);
+            lolunit_assert_doubles_equal(v1.z, v2.z, 1e-5f);
+            lolunit_assert_doubles_equal(v1.w, v2.w, 1e-5f);
+        }
+    }
+
+    lolunit_declare_test(sqt_composition_vec4)
+    {
+        /* We check that transforming a vec4 with an SQT and a
+         * second SQT yields the same result as transforming a
+         * vec4 with the product of the two SQTs. */
+        for (vec4 v0 : test_vec4s)
+        {
+            vec4 v1 = (test_sqt_1 * test_sqt_1) * v0;
+            vec4 v2 = test_sqt_1 * (test_sqt_1 * v0);
+
+            lolunit_assert_doubles_equal(v1.x, v2.x, 1e-5f);
+            lolunit_assert_doubles_equal(v1.y, v2.y, 1e-5f);
+            lolunit_assert_doubles_equal(v1.z, v2.z, 1e-5f);
+            lolunit_assert_doubles_equal(v1.w, v2.w, 1e-5f);
+        }
+    }
+};
+
+} /* namespace lol */
+