Methods and compositions are disclosed for treating swimming pool waters in order to remove one or more nutrients necessary for algal growth and to accelerate the breakdown of objectionable chloramines within chlorinated pool waters. The target nutrients of preference are those containing phosphorus or nitrogen. Phosphorus nutrients are preferably removed by ion-exchange with finely divided lanthanum carbonate, or by direct precipitation in the pool with liquid lanthanum chloride. Nitrogen nutrients (including, in particular, chloramines) may be removed (possibly with the aid of catalysts and in separate reactors). The same reagents used to scavenge phosphates are useful in this regard, the nitrogen being released from the pool water as a nitrogenous gas. To allow the fine lanthanum carbonates to be conveniently handled in the pool environment, they may be linked to larger carrier particles, such as those of diatomaceous earth, or they may be embedded within porous beads formed from polymers or gels. In this form the reagent can be either added to, retained within and backwashed from pool filters, or added directly to pools (with or without a flocculating agent) and sucked to waste after settling. A variety of formulations for these purposes is disclosed.