This paper studies the methods for changing thresholds in the absence of secure channels after the setup of threshold secret sharing schemes. First, we construct a perfect (t,n)(t,n) threshold scheme that is threshold changeable to t′>tt′>t, which is optimal with respect to the share size. This improves the scheme of Wang and Wong by relaxing the requirement from q≥n+vq≥n+v to q>nq>n with the secret-domain Fqv. But these threshold changeable schemes along with most previously known schemes turn out to be insecure under the collusion attack of players holding initial shares. By adding a broadcast enforcement term we enhance the model with collusion security and NN options of threshold change. Then we construct a computationally secure scheme under the enhanced model, which involves much shorter shares and broadcast messages than the perfect schemes. Finally, we discuss how to realize the enrollment and disenrollment of players, and particularly, how to deal with L-fold changes of access polices.