We propose a t-out-of-n Certificateless Threshold Ring Signature (CL-TRS) scheme and prove its security under a new and stronger set of security models. The models capture a new adversarial capability called User Partial Key Replacement Attack, which has been considered practical and realistic but has never been formalized before. The new scheme requires only a constant number of bilinear pairing operations for signature verification. It also has a compact signature size which is linear to the number of non-signers (i.e. n - t) rather than that of actual signers. We also propose a 1-out-of-n CL-TRS (i.e. a certificateless ring signature scheme) which has the most efficient verification among all the certificateless ring signature schemes currently known.