Despite their increasing performance, large language models still tend to reproduce training data, generate several repetitions, and focus on the most common grammatical structures and words. A possible cause is the decoding strategy adopted: the most common ones either consider only the most probable tokens, reducing output diversity, or increase the likelihood of unlikely tokens at the cost of output accuracy and correctness. In this paper, we propose a family of three new decoding methods by leveraging a mathematical analysis of the token probability distribution. In particular, the difference between consecutive, sorted probabilities can be used to avoid incorrect tokens and increase the chance of low-probable but accurate words. Experiments concerning math problem solving, extreme summarization, and the divergent association task show that our approach consistently performs at least as well as current alternatives in terms of quality and diversity.