Nonadiabatic processes play a fundamental role in the understanding of photochemical processes in excited polyatomic molecules. A particularly important example is that of radiationless electronic relaxation at conical intersections (CIs). We discuss new opportunities for controlling coupled electron–nuclear dynamics at CIs, offered by the advent of nearly single-cycle, phase-stable, mid-infrared laser pulses. To illustrate the control mechanism, a two-dimensional model of the NO2 molecule is considered. The key idea of the control scheme is to match the time scale of the laser field oscillations to the characteristic time scale of the wave packet transit through the CI. The instantaneous laser field changes the shape and position of the CI as the wave packet passes through. As the CI moves in the laser field, it 'slices' through the wave packet, sculpting it in the coordinate and momentum space in a way that is sensitive to the carrier-envelope phase of the control pulse. We find that the electronic coherence imparted on the sub-laser-cycle time scale manifests during much longer nuclear dynamics that follow on the many tens of femtosecond time scale. Control efficiency as a function of molecular orientation is analyzed, showing that modest alignment is sufficient for showing the described effects.