A simplified but very accurate method for calculating advection of mixing ratios in a mass conservative and absolutely monotonic manner in divergent or nondivergent multidimensional flows is presented. This scheme uses a second-order-accurate, upstream approximation with monotone limiters and additionally adjusts fluxes at two cell edges around local extremes of a tracer distribution to significantly improve overall advection calculations. The minor flux adjustment slightly aggregates mass around local peaks in a manner which counters the inherent numerical diffusion associated with most numerical advection algorithms when advecting poorly resolved features. When advecting tracer shapes which are resolved by fewer than 10--20 grid cells, this scheme is significantly more accurate than higher-order algorithms for a wide range of test problems. For well-resolved tracer distributions this algorithm is very accurate and usually preserves local peak and minimum values almost perfectly. The scheme is positive-definite, but negative values can be advected with no modifications. A generalized algorithm and FORTRAN subroutine is presented for advecting mixing ratios or other conservative quantities through variable-spaced grids of one to three dimensions, including deformational flows. One- and two-dimensional tests are presented and compared with other higher-order algorithms. The computational requirements of this algorithm are significantly lower than those of other higher-order and less accurate schemes. ¿ 2000 American Geophysical Union