Two new readily-biodegradable chelating agents, S,S′-ethylenediaminedisuccinate (EDDS) and iminodisuccinate (IDS) have been assessed in terms of satisfying the main desired actions of chelating agents in pulp and paper processing: (i) transition metal-ion sequestration; (ii) magnesium retention in pulp; and (iii) avoidance of ligand distraction by calcium ions; all used the Joint Expert Speciation System (JESS) chemical speciation simulation program, and compared new agents with the traditional non-readily-biodegradable agents ethylenediaminetetraacetic acid (EDTA) and NTA. The assessments were extended to investigate the effects upon the degree of transition metal sequestration of added sulphate, exogenous low molecular mass ligands, and of varying and increasing metal-ion concentrations due to inter-regional and exogenous species variations. The investigations were performed at various pulp processing stages (cooking, washing, and oxygen delignification), and at various pH values. The results are presented as Speciation Efficiency Indices (SEI), have been validated by the pulp and paper industry, and indicate that S,S′-EDDS is the best chelating agent for pulp processing in terms of chelation efficiency for (i)–(iii) above and for readily-biodegradability.