Learning meaningful behaviors in the absence of a task-specific reward function is a challenging problem in reinforcement learning. A desirable unsupervised objective is to learn a set of diverse skills that provide a thorough coverage of the state space while being directed, i.e., reliably reaching distinct regions of the environment. At test time, an agent could then leverage these skills to solve sparse reward problems by performing efficient exploration and finding an effective goal-directed policy with little-to-no additional learning. Unfortunately, it is challenging to learn skills with such properties, as diffusing (e.g., stochastic policies performing good coverage) skills are not reliable in targeting specific states, whereas directed (e.g., goal-based policies) skills provide limited coverage. In this paper, inspired by the mutual information framework, we propose a novel algorithm designed to maximize coverage while ensuring a constraint on the directedness of each skill. In particular, we design skills with a decoupled policy structure, with a first part trained to be directed and a second diffusing part that ensures local coverage. Furthermore, we leverage the directedness constraint to adaptively add or remove skills as well as incrementally compose them along a tree that is grown to achieve a thorough coverage of the environment. We illustrate how our learned skills enable to efficiently solve sparse-reward downstream tasks in navigation environments, comparing favorably with existing baselines.