The EF Effect

This feels pretty good. I found $150 a month by cutting back on utilities and cell phone bills. I know there must be more, but for now I am starting with this. If I put the $150 in the bank every month, it will take 16 months to save up the $2,500. That's not including interest, but savings are paying less than 2%, so the interest might amount to about $20 a year. Now, the whole point of an ef is to have emergency money so I won't have to turn to credit. So, a little more calculating. At $150 a month, I will have $300 available in 2 months, and $600 available in 4 months. Within 10 months, assuming I haven't had to dig into it, I will have about $1500. If I get a surprise car expense or an appliance needs repair, I won't have to turn to credit. My ef isn't for retirement or vacation or anything else. While I would like to hold on to it, I plan to use it instead of a credit card to meet unexpected expenses.
But, back to the quandry. Can I save for an emergency while getting started on debt reduction? I don't know yet. So far my expense cutting has resulted in extra money for savings, not debt reduction. Where can I find that?
I am going to take a look at my monthly payments. I have been paying the same amount on most of them for a long time, not taking into account that the minumums have gone down as the balances went down. Maybe it's not much, but I want to look at what I am already paying and see if I can juggle that around to pay down the debt faster, without adding to our expenses.
What would you do? Do you think this is any better than any other plan?