I use two savings accounts.

One is my longterm emergency fund and I try to never touch it. The other covers all my sinking funds – I use Quicken to make sure there’s enough in there for everything.
One place where I disagree with DR a little bit is I think $1000 is too small a BEF for many people. I have heard DR on the podcast suggesting to particular individuals that they increase theirs. There are certain “emergencies” that are very predictable. For example the Car Talk guys suggest that an old car takes $600-$1200/year for repairs. If you have an old car I think you should aim for a BEF that’s big enough to cover $1200 in repair PLUS $1000 for the unpredictable. If you raise animals, have enough to cover a year’s average surprise vet bills. That sort of thing. You know it’s going to happen even if you can’t say when.
After I did my budget for a few years, some years back, I was able to come up with a number for my average “one time” and surprise expenses, mostly predictable. The vet, car repair, some sort of home repair, medicine, fees, holiday gifts, life insurance..I added all that irregular stuff up and divided by 12 and I put *at least* that much into the sinking savings fund each month. And then, it’s not an emergency because I have the money to cover it. Even if you’re in debt, I think it’s worth having a slightly bigger cushion so that two things in a row don’t knock you into more debt.