CHICAGO—The number of shooting deaths here has surpassed the total for last year with four months still to go, in a bloody 2016 in which Chicago has outpaced most major U.S. cities in homicides.

Police are stepping up efforts to confiscate illegal firearms from the streets, and the state recently passed a law toughening penalties for gun trafficking, but the moves so far seem to be having little effect, with this August shaping up to be the most violent in almost two decades.

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