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This paper discusses methods for generating RSA moduli with a predetermined portion. Predetermining a portion enables to represent RSA moduli in a compressed way, which gives rise to reduced transmission- and storage requirements. The first method described in this paper achieves the compression rate of known methods but is fully compatible with the fastest prime generation algorithms available on constrained devices. This is useful for devising a key escrow mechanism when RSA keys are generated on-board by tamper-resistant devices like smart cards. The second method in this paper is a compression technique yielding a compression rate of about 2/3 instead of 1/2. This results in higher savings in both transmission and storage of RSA moduli. In a typical application, a 2048-bit RSA modulus can fit on only 86 bytes (instead of 256 bytes for the regular representation). Of independent interest, the methods for prescribing bits in RSA moduli can be used to reduce the computational burden in a variety of cryptosystems.