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Should workers be provided with insurance against search‐induced wage fluctuations? To answer this question, I rely on the numerical simulations of a model of on‐the‐job search and precautionary savings. The model is calibrated to low‐skilled workers in the United States. The extent of insurance is determined by the degree of progressivity of a non‐linear transfer schedule. The fundamental trade‐off is that a more generous provision of insurance reduces incentives to search for better‐paying jobs, which increases the cost of providing insurance. I show that progressivity raises the search intensity of unemployed workers, which reduces the equilibrium rate of unemployment, but it lowers the search intensity of employed job seekers, which reduces the output level. I also solve numerically for the optimal non‐linear transfer schedule. The optimal policy is to provide little insurance up to a monthly income level of $1350, so as to preserve incentives to move up the wage ladder, and nearly full insurance above $1450. This policy reduces the standard deviation of labor income net of transfers by 34 per cent and generates a consumption‐equivalent welfare gain of 0.7 per cent. The absence of private savings does not fundamentally change the shape of the optimal transfer function, but tilts the optimal policy towards more insurance, at the expense of a less efficient allocation of workers across jobs.