Change in marital fertility in 407 Prussian Kreise from 1875 to 1910 is modeled to depend on the gap between the number of desired surviving births, N*, divided by child survival, s, and the number that would be born under natural marital fertility, M, given the age at marriage. Some fraction of this gap is averted, depending on the propensity to avert unwanted births, D. Although none of these components is observed directly, we can estimate each indirectly under strong assumptions. Decline in N*/s accounts for twice as much of the decline in fertility as does an increase in D. Natural fertility rose during the period. Unwanted births increased slightly, despite a tripling of births averted. The most important causes of decline in N* were increases in female labor supply, real income, and health workers. A rising level of education is the most important cause of increasing propensity to avert births. Demand-side changes were important causes of the transition, but changes in readiness to contracept also were important, as was the interaction of the two.