DykerNewbie, big_city_beth, settle in because level billing does not lower what you owe over 12 months. It just re-shuffles when you owe it.
ConEd's level billing (budget billing) takes an average of the past 12 months' usage at the service address, sometimes adjusted for weather and projected rates, and bills you roughly the same amount each month. Then, depending on your plan, there's either a periodic true-up or a final month where the difference between your actual usage and what you've paid is settled. You can end up with a credit or a balance due in that catch-up month.
In my experience renting in an old building with one window AC, level billing was great for avoiding a July surprise and a February shock when the gas heat ran old radiators. But the March true-up was annoying the first year: I had been paying below actual during a cold snap and owed a noticeable catch-up amount. The opposite can happen too—if you run the AC less, you might be credited.
Caveats: If your service address has limited history, the initial average may be based on an estimate from a similar property or the previous occupant, which is exactly what big_city_beth is asking. You can call ConEd and ask them to review the first level amount, especially if the unit was vacant or the prior tenant had very different habits. You should still submit your own readings if you can; do not rely on estimated reads forever.
For a small apartment, I'd say level billing is more of a budgeting tool, not a savings one. If you'd rather know exactly what you're using, pay actual and set aside extra for summer. If you want predictable monthly expenses, level billing is fine. Just don't call it a discount.