A tuneable and interpretable method for relaxing the instrumental variables (IV) assumptions to infer treatment effects in the presence of unobserved confounding. For a treatment-associated covariate to be a valid IV, it must be (a) unconfounded with the outcome and (b) have a causal effect on the outcome that is exclusively mediated by the exposure. There is no general test of the validity of these IV assumptions for any particular pre-treatment covariate. However, if different pre-treatment covariates give differing causal effect estimates when treated as IVs, then we know at least some of the covariates violate these assumptions. 'budgetIVr' exploits this fact by taking as input a minimum budget of pre-treatment covariates assumed to be valid IVs and idenfiying the set of causal effects that are consistent with the user's data and budget assumption. The following generalizations of this principle can be used in this package: (1) a vector of multiple budgets can be assigned alongside corresponding thresholds that model degrees of IV invalidity; (2) budgets and thresholds can be chosen using specialist knowledge or varied in a principled sensitivity analysis; (3) treatment effects can be nonlinear and/or depend on multiple exposures (at a computational cost). The methods in this package require only summary statistics. Confidence sets are constructed under the "no measurement error" (NOME) assumption from the Mendelian randomization literature. For further methodological details, please refer to Penn et al. (2024) <doi:10.48550/arXiv.2411.06913>.