The first experiments to study the shell's controlled asymmetry of capsule with DT-fuel in a highly symmetrical X-ray field, which is obtained inside a spherical hohlraum, were implemented. The asymmetry results from the coating of one hemisphere with the additional layer of material. The main goal of the experiment was to define the value of the capsule asymmetry, allowing us to experimentally obtain the neutron yield, which would be very different from the yield obtained in the experiment with the spherically symmetrical shell having the same mass as the asymmetrical one. It was shown that the shell asymmetry of ∼50% leads to the ∼(2–4) times reduction of the neutron yield as compared with the symmetrical shell. 2D calculations of the asymmetric capsule compression, using the MIMOZA-ND code, were conducted. The calculations demonstrated that the compression of targets, when exploding pusher regime occurs has a complicated character. The computational neutron yield, and the delay of the neutron generation time are in good agreement with the experimental data.