Experimental and theoretical investigations were made of the characteristics of the interaction between solid targets and picosecond laser pulses with a complex profile. A prepulse preceding the main picosecond pulse increased the absorption of the s-polarised radiation and reduced the absorption of p-polarised radiation. Moreover, the prepulse made it possible to control the intensity of various components of the x-ray radiation emitted by the laser plasma. A satisfactory agreement between the experimental results and numerical calculations was obtained and a theoretical optimisation of the efficiency of x-ray generation was made.