SPDZ (pronounced “Speedz”) is the nickname of the MPC protocol of Damgard et al. from Crypto 2012. SPDZ provided various efficiency innovations on both the theoretical and practical sides compared to previous work in the preprocessing model. In this paper, the authors resolve a number of open problems with SPDZ; and present several theoretical and practical improvements to the protocol. In detail, they start by designing and implementing a covertly secure key generation protocol for distributed BGV secret keys. In prior work this was assumed to be provided by a given setup functionality. Protocols for distributing BGV secret keys are likely to be of wider applicability than to the SPDZ protocol alone.