Recent advances have allowed Deep Spiking Neural Networks (SNNs) to perform at the same accuracy levels as Artificial Neural Networks (ANNs), but have also highlighted a unique property of SNNs: whereas in ANNs, every neuron needs to update once before an output can be created, the computational effort in an SNN depends on the number of spikes created in the network. While higher spike rates and longer computing times typically improve classification performance, very good results can already be achieved earlier. Here we investigate how Deep SNNs can be optimized to reach desired high accuracy levels as quickly as possible. Different approaches are compared which either minimize the number of spikes created, or aim at rapid classification by enforcing the learning of feature detectors that respond to few input spikes. A variety of networks with different optimization approaches are trained on the MNIST benchmark to perform at an accuracy level of at least 98%, while monitoring the average number of input spikes and spikes created within the network to reach this level of accuracy. The majority of SNNs required significantly fewer computations than frame-based ANN approaches. The most efficient SNN achieves an answer in less than 42% of the computational steps necessary for the ANN, and the fastest SNN requires only 25% of the original number of input spikes to achieve equal classification accuracy. Our results suggest that SNNs can be optimized to dramatically decrease the latency as well as the computation requirements for Deep Neural Networks, making them particularly attractive for applications like robotics, where real-time restrictions to produce outputs and low energy budgets are common.