In this paper, we refer to social autonomy in a collaborative relationship among agents based on delegation and help. We address the problem of adjustable autonomy, i.e., we discuss when modifying the assigned/received delegation entails a corresponding enlargement or restriction of autonomy and at which level. We stress in particular the role played in autonomy by: 1) the degree of "openness" of delegation (execution autonomy), 2) the allowed initiative in (re)starting negotiation (meta-autonomy), 3) the degree and kind of control (feedback+intervention), and 4) the strength of delegation with respect to interaction. We show how the adjustability of delegation and autonomy is actually "bilateral," because not only the user (delegator, trustor, client) can adjust the autonomy of the agent (delegee, trustee, contractor), but the agent can also have (cooperative) reasons for and the ability to change the received delegation and modify its own autonomy in it. Adjustment is also "bidirectional" (from more autonomy to less autonomy, or vice versa), and multidimensional. Finally, we analyze some reasons for modifying the assigned autonomy and show how the adjustment of autonomy depends-on the delegator's side-on a crisis of trust ; vice versa, the delegee's adjustment of its own autonomy depends on some disagreement about the trust received from the delegator, and, in particular, either a higher or lower confidence in itself or in external circumstances. Some preliminary hints about necessary protocols for adjusting the interaction with agents are provided. This work is neither directly prescriptive nor simply descriptive. It is aimed at providing a theoretical framework, i.e., the conceptual instruments necessary for analyzing and understanding interaction with autonomous entities.