A method for removing impurities from a waste solid to provide at least a portion of a suitable crystallizer feed to a process for making crystalline sodium carbonate, bicarbonate, and/or other derivatives. The method comprises: contacting the waste solid with a leach solution to dissolve at least one impurity and dissolving the resulting leached residue. Leaching may include heap percolation. The leach solution may comprise a crystallizer purge liquor, a process waste effluent, a mine water, or mixtures thereof. The method may further comprise adding a magnesium compound to the resulting leached residue during or after its dissolution to remove another impurity. The waste solid preferably comprises a pond solid containing such impurities. The pond solid may be recovered from a pond receiving crystallizer purge liquor(s) and/or other process waste effluent(s). The pond solid may contain sodium carbonate, any hydrate thereof, sodium bicarbonate, and/or sodium sesquicarbonate. The impurities to be removed may comprise sodium chloride, sodium sulfate, silicates, and/or organics.