Conductivity doping of organic semiconductors is an essential prerequisite for many organic devices, but the specifics of dopant activation are still not well understood. Using many-body simulations that include Coulomb interactions and dopant ionization/de-ionization events explicitly we here show significant doping efficiency even before the electron affinity of the dopant exceeds the ionization potential of the organic matrix (p-doping), similar to organic salts. We explicitly demonstrate that the ionization of weak molecular dopants in organic semiconductors is a disorder-, rather than thermally induced process. Practical implications of this finding are a weak dependence of the ionized dopant fraction on the electron affinity of the dopant, and an enhanced ionization of the weak dopants upon increasing dopant molar fraction. As a result, strategies towards dopant optimization should aim for presently neglected goals, such as the binding energy in host-dopant charge-transfer states being responsible for the number of mobile charge carriers. Insights into reported effects are provided from the analysis of the density of states, where two novel features appear upon partial dopant ionization. ... mehrThe findings in this work can be used in the rational design of dopant molecules and devices.