We investigate the effect of different model architectures, training objectives, hyperparameter settings and decoding procedures on the diversity of automatically generated image captions. Our results show that 1) simple decoding by naive sampling, coupled with low temperature is a competitive and fast method to produce diverse and accurate caption sets; 2) training with CIDEr-based reward using Reinforcement learning harms the diversity properties of the resulting generator, which cannot be mitigated by manipulating decoding parameters. In addition, we propose a new metric AllSPICE for evaluating both accuracy and diversity of a set of captions by a single value.