Methods are provided for treating suspensions of particles to improve the drainage rate and/or the solids content of flocs of the particles. The method includes the steps of (i) providing a suspension which comprises particles in a fluid; (ii) adding a cyclodextrin compound to the suspension; and (iii) dewatering the suspension by removing at least a portion of the fluid to form a cake comprising the particles. The cyclodextrin compound desirably is added in an amount effective to increase the dewatering rate of the flocs, to increase the solids content, or both, over that rate, solids content, or both, that would be obtained without the addition of the cyclodextrin compound. The suspension may be, for example, a biological or non-biological sludge, or a suspension of pulp fibers, such as in a pulping or papermaking process.