Deep convection associated with thunderstorms and sometimes with frontal systems is an effective way to transport material from the planetary boundary layer to the upper troposphere and even to the lower stratosphere. Aerosol particles observed in clouds and in cloud outflows suggest that deep convection is an important source of particles in the upper troposphere. However, the detailed pathways by which the observed small particles could have been formed inside the clouds are unknown. In this paper we propose a hypothesis, where water insoluble trace gases that can survive the deep convective updraft are producing new particles at low temperatures near the tropopause. In order to be able to verify this new mechanism, laboratory experiments were designed to simulate this process. It was found that ambient water insoluble trace gases were indeed able to produce new aerosol particles by homogeneous nucleation under cloud like conditions. Therefore it seems that our hypothesis gives a plausible explanation for new particle production inside cloud anvils and cloud outflows.