A method for making swellable particles, wherein "swellable" means that a compound can be found that is readily absorbed by a particle such that the particle is larger after absorbing the compound than before absorbing the compound said method comprising: mixing a) initial particles that comprise polymer, b) at least one monomer, c) at least one oil-soluble initiator, and d) at least one chain-transfer agent, wherein said mixing is performed under conditions in which said monomer is capable of forming oligomer or polymer or a mixture thereof, i.e. conditions that, if held constant for one hour, without adding or removing any ingredients, 5% or more of said monomer, based on the weight of monomer present at the beginning of the one hour period, will react to form oligomer or polymer or a mixture thereof, wherein said oil-soluble initiator has solubility in water, by weight based on the weight of water, of 1% or less, wherein none of said monomer is mixed with said initial particles prior to establishing said conditions in which said monomer is capable of forming oligomer or polymer or a mixture thereof, wherein all of said monomers have solubility in water at 25°C of 1% or less by weight based on the weight of the water, and wherein the amount of chain-transfer agent is 5% or more by weight based on the total weight of the monomers, and polymerizing said monomers to form at least one oligomer or polymer or mixture thereof. mixing a) initial particles that comprise polymer, b) at least one monomer, c) at least one oil-soluble initiator, and d) at least one chain-transfer agent, wherein said mixing is performed under conditions in which said monomer is capable of forming oligomer or polymer or a mixture thereof, i.e. conditions that, if held constant for one hour, without adding or removing any ingredients, 5% or more of said monomer, based on the weight of monomer present at the beginning of the one hour period, will react to form oligomer or polymer or a mixture thereof, wherein said oil-soluble initiator has solubility in water, by weight based on the weight of water, of 1% or less, wherein none of said monomer is mixed with said initial particles prior to establishing said conditions in which said monomer is capable of forming oligomer or polymer or a mixture thereof, wherein all of said monomers have solubility in water at 25°C of 1% or less by weight based on the weight of the water, and wherein the amount of chain-transfer agent is 5% or more by weight based on the total weight of the monomers, wherein said mixing is performed under conditions in which said monomer is capable of forming oligomer or polymer or a mixture thereof, i.e. conditions that, if held constant for one hour, without adding or removing any ingredients, 5% or more of said monomer, based on the weight of monomer present at the beginning of the one hour period, will react to form oligomer or polymer or a mixture thereof, wherein said oil-soluble initiator has solubility in water, by weight based on the weight of water, of 1% or less, wherein none of said monomer is mixed with said initial particles prior to establishing said conditions in which said monomer is capable of forming oligomer or polymer or a mixture thereof, wherein all of said monomers have solubility in water at 25°C of 1% or less by weight based on the weight of the water, and wherein the amount of chain-transfer agent is 5% or more by weight based on the total weight of the monomers, and polymerizing said monomers to form at least one oligomer or polymer or mixture thereof.