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Measurements of any property of a microscopic system are bound to show significant deviations from the average, due to thermal fluctuations. For time-integrated currents such as heat, work or entropy production in a steady state, it is in fact known that there will be long stretches of fluctuations both above as well as below the average, occurring equally likely at large times. In this paper we show that for any finite-time measurement in a non-equilibrium steady state - rather counter-intuitively - fluctuations below the average are more probable. This discrepancy is higher when the system is further away from equilibrium. For overdamped diffusive processes, there is even an optimal time when time-integrated current fluctuations mostly lie below the average. We demonstrate that these effects result from the non-monotonic skewness of current fluctuations and provide evidence that they are easily observable in experiments. We also discuss their extensions to discrete space Markov jump processes and implications to biological and synthetic microscopic engines.