An accelerator powder for cement and also rapid-setting binder compositions which contain the accelerator powder and the use in mortar or concrete. The accelerator powder includes from 10 to 99.7% by weight of a water-insoluble mineral powder P and from 0.3 to 90% by weight of at least one compound V selected from the group consisting of alkali metal halides and alkaline earth metal halides, alkali metal nitrates and alkaline earth metal nitrates, alkali metal nitrites and alkaline earth metal nitrites, alkali metal thiocyanates and alkaline earth metal thiocyanates and hydroxyalkylamines or salts thereof, and mixtures thereof.