We show that avoiding bends in a current-carrying superconducting nanowire enhances the probability for low energy photons to be detected and that this enhancement is entirely due to the increase in the experimentally achievable critical current. We studied nanowires shaped as either meander or spiral. The spirals had different layouts, a double-spiral layout with an S-turn in the middle and a single-spiral layout without such turn. Nanowires were prepared from films of niobium nitride with a thickness of 5 nm. For specimens with each layout we measured the spectra of the single-photon response in the wavelength range from 400 nm to 1600 nm and defined the cut-off wavelength (λc) beyond which the response rolls off. The largest and the smallest λc were found for the single-spiral layout and for the meander, respectively. For all three layouts the relationship between λc and the relative bias current falls onto a universal curve which has been predicted earlier in the framework of the modified hot-spot model. For the single-spiral layout, the efficiency of photon detection at wavelengths smaller than λc reaches the expected absorbance of the spiral structure and the timing jitter per unit length of the nanowire has the smallest value.