Not much info given Kivi. Factors to consider may be access, depth of fill, material gradation, water content, desired result, etc..
One method I've used and seen done before is Deep Dynamic Compaction (DDC). This is the simple brute force method of dropping large weights (10 to 30 ton) from a crane in a grid type pattern to cover the site and densify the soils down to 20 or 30-ft. Simple but it works and is not too costly.
INCO has used this at its Sudbury site and there were some papers on in in CIM Journal for late 2000. UK MIRO also has some papers on this. If this is dredge product rather than spigotted tailings you may want to dry it first as the clay content will certainly affect "squeezability"