We consider a non-parametric model for estimating the effect of a binary treatment on an outcome variable while adjusting for an observed covariate. A naive procedure consists of performing two separate non-parametric regressions of the response on the covariate: one with the treated individuals and the other with the untreated. The treatment effect is then obtained by taking the difference between the two fitted regression functions. This article proposes a backfitting algorithm that uses all the data for the two abovementioned non-parametric regressions. We give finite sample theoretical results showing that the resulting estimator of the treatment effect can have lower variance. This improvement is not necessarily achieved at the cost of a larger bias. In all of the performed simulations, we observe that mean squared error is substantially lower for the proposed backfitting estimator. When more than one covariate is observed, our backfitting estimator can still be applied by using the propensity score (the probability of being treated for a given setup of the covariates). We illustrate the use of the backfitting estimator in a several-covariate situation with data on a training program for individuals having faced social and economic problems.