In this paper, firstly we propose two new concepts concerning the notion of key escrow encryption schemes: provable partiality and independency. Roughly speaking we say that a scheme has provable partiality if existing polynomial time algorithm for recovering the secret knowing escrowed information implies a polynomial time algorithm that can solve a well-known intractable problem. In addition, we say that a scheme is independent if the secret key and the escrowed information are independent. Finally, we propose a new verifiable partial key escrow, which has both of above criteria. The new scheme use McCurley encryption scheme as underlying scheme.