Summary: This paper presents the concept of k-FR circuits. The controllability of such a circuit is high due to its special structure. It is shown that all stuck-at faults and stuck-open faults in a k-FR circuit can be detected and located by k(k1)1 test vectors under the highly observable condition which assumes the output of every gate to be observable. k is usually two or three. This paper also presents an algorithm for converting an arbitrary combinational circuit into a k-FR circuit. A k-FR circuit is easy to test when using technologies such as the electron-beam probing, the current measurement, or the CrossCheck testability solution.