We study the laser-driven generation of thermonuclear neutrons from targets with a microstructured surface in the form of deuterated microwires, using three-dimensional numerical simulation with previously obtained results of large-scale structural optimization of the target, which provides its best heating by femtosecond laser pulses of moderate intensity. We show that, for modern laser technologies, femtosecond lasers of low (several mJ) energy are even better for creating a neutron source than more powerful (∼1 J) lasers because the mode of high (∼1 kHz) pulse repetition rate is practically available. Microlayers (relief) and cylindrical microholes on the irradiated side are considered as alternative microstructured targets. For the latter, we demonstrate accumulation of ions on the axis of the holes, which leads to increase in the ion density above the initial value and consequently to a possible increase in the yield of thermonuclear neutrons.