Small-scale dynamos play important roles in modern astrophysics, especially on Galactic and extragalactic scales. Owing to dynamo action, purely hydrodynamic Kolmogorov turbulence hardly exists and is often replaced by hydromagnetic turbulence. Understanding the size of dissipative magnetic structures is important in estimating the time scale of Galactic scintillation and other observational and theoretical aspects of interstellar and intergalactic small-scale dynamos. Here we show that the thickness of magnetic flux tubes decreases more rapidly with increasing magnetic Prandtl number than previously expected. Also the theoretical scale based on the dynamo growth rate and the magnetic diffusivity decrease faster than expected. However, the scale based on the cutoff of the magnetic energy spectra scales as expected for large magnetic Prandtl numbers, but continues in the same way also for moderately small values -contrary to what is expected. For a critical magnetic Prandtl number of about 0.27, the dissipative and resistive cutoffs are found to occur at the same wavenumber. For large magnetic Prandtl numbers, our simulations show that the peak of the magnetic energy spectrum occurs at a wavenumber that is twice as large as previously predicted.