ABSTRACT Modelling the growth histories of specific galaxies often involves generating the entire population of objects that arise in a given cosmology and selecting systems with appropriate properties. This approach is highly inefficient when targeting rare systems such as the extremely luminous high-redshift galaxy candidates detected by JWST. Here, we present a novel framework for generating merger trees with branches that are guaranteed to achieve a desired halo mass at a chosen redshift. This method augments extended Press Schechter theory solutions with constrained random processes known as Brownian bridges and is implemented in the open-source semi-analytic model galacticus. We generate ensembles of constrained merger trees to predict the growth histories of seven high-redshift JWST galaxy candidates, finding that these systems most likely merge ≈2 Gyr after the observation epoch and occupy haloes of mass ≳1014 M⊙ today. These calculations are thousands of times more efficient than existing methods, are analytically controlled, and provide physical insights into the evolution of haloes with rapid early growth. Our constrained merger tree implementation is publicly available at https://github.com/galacticusorg/galacticus.