Synthesizing finite-state systems from full linear-time temporal logic (LTL) is an ambitious way to tackle the challenge of constructing correct-by-construction systems. One particularly promising approach in this context is bounded synthesis, originally proposed by Schewe and Finkbeiner, which in turn builds upon Safraless synthesis, as described by Kupferman and Vardi. Previous implementations of these approaches performed the computation either in an explicit way or used symbolic data structures other than binary decision diagrams (BDDs). In this paper, we reconsider BDDs as state space representation and use it as data structure for bounded synthesis. The key to this construction is the application of two novel optimisation techniques that decrease the number of state bits in such a representation significantly. The first technique uses signalling bits to connect sub-games representing the safety- and non-safety parts of the specification. The second technique is based on a closer analysis of the step of building a safety game from a universal automaton and uses a sufficient condition to remove some so-called counters from the state space of the game. We evaluate our approach on several benchmark suites and show that the new approach leads to a computation time improvement of several orders of magnitude.