I've been raised angel money as CEO several times, and also advised angels on multiple transactions...

Of course the investors understand that you don't want to "give away too much" equity, but of course if they believe in your business then they'll want to acquire a meaningful position.

If you're still pre-revenue (or even if you have revenue but still negative cash-flow), then the thought-process in the angel mind often goes like this:

1. How much money does this company need, to significantly transform itself to the next stage (and either become cash-flow-positive or at least become a serious candidate for a much larger round of funding)?

2. For my risk, I'm going to take around a third. (Maybe 20-40%).

3. Therefore, if I think this company needs $400k to hit its next milestone, and I want to take 40%, then I'm going to give this company a pre-money valuation of $1M.

And then, of course, the question is, "do I think it's ok to risk $400k on this enterprise."

If you were to counter-offer to an investor, "gee, thanks, but we don't want to give away that big a %age — so we're only going to take $200k," the investor would have a huge problem:

The angel would say, "but you just got done telling me that the company absolutely needs $400k to grow! so, if you 'settle' for $200k, won't you be in trouble? or were you lying when you said you needed a full $400k?"

It can become a bit of a catch-22 if you start down this road.

RECOMMENDATION:

Figure out what you truly think the company needs, to really transform itself into something much bigger. Try to raise that much in the round. LISTEN to the feedback you hear from angels. They will drop hints (or tell you explicitly) if they think you're asking too much or too little. If your round is over-subscribed, that is, if you're able to get more investors than you needed, then you can run up the $ valuation. Otherwise, keep it modest and expect the early risk-takers to eat a big chunk of equity.

But don't counter-offer a lower amount of money for the round, because it would discredit your earlier claims about what you need.

Of course I'd be happy to jump onto a call and discuss this further if you like. And above I was pretty much assuming you're pre-revenue; I would change some of what I said if you have positive cash flow or at least some revenue.