Fibring is recognized as one of the main mechanisms for combining logics. General results for preservation of soundness and completeness have been established. However, although quite powerful, fibring suffers from an anomaly usually known as the collapsing problem. Indeed, ever since the first accounts of fibring, it could be noticed that fibring of classical with intuitionistic logic would collapse into just classical logic. In this work, we propose a solution to solve this problem by adopting a more general notion of fibred semantics using cryptomorphisms. In particular, we show that the novel notion of cryptofibring encompasses the original definition of fibred model, while admiting also (initial) amalgamated models that can be used to show that the above mentioned collapse is no longer present. We also show that the general results for preservation of soundness and completeness by fibring can be extended to this wider setting. Conservativeness issues are also addressed. Joint work with Carlos Caleiro.