A method for making secondary swellable particles, said method comprising the steps of: making swellable initial particles by a method comprising mixing (a) initial particles of any material in particulate form, (b) at least one monomer, (c) at least one initiator, and (d) at least one chain-transfer agent, wherein said mixing of said (a), (b), (c), and (d) is performed under conditions in which said monomer (b) forms oligomer or polymer or a mixture thereof, and subsequent to said step, the step of mixing (e) said swellable initial particles produced in said step, (f) at least one monomer, wherein any or all of said monomer (f) may be the same as said monomer (b), different from said monomer (b), or a mixture thereof, (g) at least one oil-soluble initiator having a solubility in water, by weight based on the weight of water, of 1% or less, wherein any or all of said initiator (g) may be the same as said initiator (c), different from said initiator (c), or a mixture thereof, and (h) at least one chain-transfer agent, wherein any or all of said chain-transfer agent (h) may be the same as said chain-transfer agent (d), different from said chain-transfer agent (d), or a mixture thereof, wherein said mixing of said (e), (f), (g), and (h) is performed under conditions in which said monomer (f) is capable of forming and does form oligomer or polymer or a mixture thereof; 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; and wherein "conditions in which said monomer (f) is capable of forming and does form oligomer or polymer or a mixture thereof" are 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. making swellable initial particles by a method comprising mixing (a) initial particles of any material in particulate form, (b) at least one monomer, (c) at least one initiator, and (d) at least one chain-transfer agent, wherein said mixing of said (a), (b), (c), and (d) is performed under conditions in which said monomer (b) forms oligomer or polymer or a mixture thereof, and (a) initial particles of any material in particulate form, (b) at least one monomer, (c) at least one initiator, and (d) at least one chain-transfer agent, subsequent to said step, the step of mixing (e) said swellable initial particles produced in said step, (f) at least one monomer, wherein any or all of said monomer (f) may be the same as said monomer (b), different from said monomer (b), or a mixture thereof, (g) at least one oil-soluble initiator having a solubility in water, by weight based on the weight of water, of 1% or less, wherein any or all of said initiator (g) may be the same as said initiator (c), different from said initiator (c), or a mixture thereof, and (h) at least one chain-transfer agent, wherein any or all of said chain-transfer agent (h) may be the same as said chain-transfer agent (d), different from said chain-transfer agent (d), or a mixture thereof, wherein said mixing of said (e), (f), (g), and (h) is performed under conditions in which said monomer (f) is capable of forming and does form oligomer or polymer or a mixture thereof; 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; and wherein "conditions in which said monomer (f) is capable of forming and does form oligomer or polymer or a mixture thereof" are 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. (e) said swellable initial particles produced in said step, (f) at least one monomer, wherein any or all of said monomer (f) may be the same as said monomer (b), different from said monomer (b), or a mixture thereof, (g) at least one oil-soluble initiator having a solubility in water, by weight based on the weight of water, of 1% or less, wherein any or all of said initiator (g) may be the same as said initiator (c), different from said initiator (c), or a mixture thereof, and (h) at least one chain-transfer agent, wherein any or all of said chain-transfer agent (h) may be the same as said chain-transfer agent (d), different from said chain-transfer agent (d), or a mixture thereof,