A small perturbation analysis is made of the flow inside a spherical explosion created in a gas absorbing energy from an array of lasers with a common focus. The influence of a small counterpressure outside the leading shock wave is investigated for power deposition constant in time. The departure from self-similarity is described by a power series in the variable y, the inverse square of a Mach number based on the wave-front velocity. To first order, the flow equations are solved numerically, the shock velocity is obtained and the radial profiles of velocity, density and pressure are presented graphically. The flow singularity at the radiation focus is discussed.