Reducing the swaps to specific granular amounts helps prevent this by making the units as indistinct as possible.

If five people go to a party, and one person has a 3-dollar bill, another person has a 17-dollar bill, and the others have equally unusual amounts, then it is clear how this idea is going to be ineffective.  And these weird denominations of bills are exactly like how Bitcoin works internally.  But that is why sticking to some standard swap denominations is important (as I suggested with 1, 5, 25, etc.).

if before everyone gets to the party, they exchange their unusual denominations for one-dollar bills, and then exchange 1:1 all evening, someone who hands you 5 of them isn't going to reveal any information on the basis of which 5 one-dollar bills you got, other than that one person came to the party with at least five dollars.  For all intents and purposes they are equally anonymous.

If I am an anonymizing Bitcoin client and somebody sends me 73.26 BTC, the first thing I will do is split that into 25+25+5+5+5+5+1+1+1+.20+.04 and I will probably discard the remaining 0.02 as a transaction fee somewhere so long as it's not worth mixing.  Then, all of those chunks will be traded with others, one-for-one.  By the time each chunk has been traded six or seven times, what's a recipient going to learn to know that for example three chunks of five were combined to make fifteen?  Not much of use.

One could perform an analysis on those three chunks to see if they might happen to all share a common possible point of origin on the block chain (an intersection attack), which could identify the original origin.  But that could be easily mitigated just by the client occasionally "mixing" same-sized chunks with itself, which is indistinguishable from mixing with others, and which would make the ancestry of each chunk look very "inbred" so to speak, and therefore poorly useful for confidently identifying distinct faraway ancestors.