Scholarship on algorithms has drawn on the analogy between algorithmic systems and bureaucracies to diagnose shortcomings in algorithmic decision-making. We extend the analogy further by drawing on Michel Crozier's theory of bureaucratic organizations to analyze the relationship between algorithmic and human decision-making power. We present algorithms as analogous to impartial bureaucratic rules for controlling action, and argue that discretionary decision-making power in algorithmic systems accumulates at locations where uncertainty about the operation of algorithms persists. This key point of our essay connects with Alkhatib and Bernstein's theory of 'street-level algorithms', and highlights that the role of human discretion in algorithmic systems is to accommodate uncertain situations which inflexible algorithms cannot handle. We conclude by discussing how the analysis and design of algorithmic systems could seek to identify and cultivate important sources of uncertainty, to enable the human discretionary work that enhances systemic resilience in the face of algorithmic errors.