I don't really do a monthly budget. Instead, I keep track of our annual expenses for all categories in a spreadsheet (I pull the totals from Mint at the end of each year, and then I update the inflation rates for all the previous years to convert all the totals into today's dollars).
Then I basically average each category that makes sense (some, like rent, are "fixed" by external factors and I do not do the average function there). This gives me our natural amount of spending for each category that takes into account those random unknowns or large, infrequent purchases.
If any category total gives me pause, then DH and I might decide to keep a closer eye on those types of purchases in the coming year. But we don't restrict that category by setting a strict budget.
Then, using these historical numbers, I can take what I know we will likely spend (based on our historical patterns) in a year, and also our expected tax bill (using MDMs case study spreadsheet), and subtract those outflows from our annual salaries to get our surplus, which I then can allocate to fill up our pre-tax, post tax, and other savings vehicles. Now that I know how much goes into each savings vehicle, I then set up the monthly autodrafts from our bank account.
So, from our salaries, taxes are taken out before the paychecks hit our account. As soon as our paychecks come in, the savings autodrafts pull a bunch out. What is leftover after everything is taken out is essentially exactly what we will be spending on average during a month. So we just spend that like we normally do, and since our "planned" spending reflects our historical spending, we are basically always right on target.
edit: if at the end of the year, we've underspent what I projected for our annual spending, I hold onto that cash until after Jan 1 and then put that annualized surplus into our IRAs. And this new, lower spending year will then be reflected in the new averages that I use to plan the upcoming year's spending/saving. Essentially, this "budgeting" activity is entirely so I can plan exactly how much I can save (and in what accounts). Doing so accurately requires an accurate projection of our spending and tax bill so I can take that money out of consideration. Then it's just a matter of 'set and forget'.
I also do have mint set up with the budget feature with my annual spending targets (divided by 12 to get our monthly averages) for each category. But I never worry when a certain category goes over because we frequently buy items in bulk or take advantage of end-of-season sales, which over the course of the year, is cheaper. I check mint daily, and take a cursory glance at the how our spending is doing in relation to our budget (Mint has "buckets" which are filled as transactions with that category label come through). This helps me keep on top of any transactions that might have been automatically mis-categorized so our spending plan can be as accurate as possible.
edit2: I just realized I didn't really answer your question! ok, so how parts of this method could help you achieve a higher savings rate:
--our annual spending plan is kind of a big financial meeting between DH and I. We go over this years spending and talk about what went well, and what didn't. What changes do we want to make this coming year? And then we may set some lower spending targets for certain categories that we aren't currently happy with.
--so that means when I'm planning our yearly spending, the plan is a combination of historical spending habits but also realistic spending goals. Based on what our spending for a certain category "felt like" this year, and compared to other years, we can kind of tell how much we could reasonably adjust that same category the coming year. We can pick up to 3 categories to adjust; any more than that and it is too much change to be sustainable. (It just happens that the last few years, we haven't felt the need to adjust our historical spending numbers to have goals; we are happy with the averages as they are.)
--In mint, I can set my "target" category budget as this lower target number for a category I want to keep my eye on day to day.
--only having one month's worth of expenses (after pulling out our savings first!) sitting in our bank account seems to emulate a variation of the envelope method. This is the amount we get to spend this month and that's it--once it's gone, its gone.