How do I keep the costs from running away?

Almost every overrun comes from scope that grew without anyone writing it down. Not from rates being too high, and rarely from a wrong estimate.

How it happens in practice

The pattern is always the same. A request comes up in a meeting, someone calls it "a small change", and the agency does it. Ten small changes later an invoice arrives that nobody expected, and the conversation is then about the invoice rather than about the ten moments where someone should have said this fell outside.

Nobody acted badly on either side. The agency wanted to be helpful, you wanted to move forward.

The rule that fixes this

Every extension gets a written estimate before work starts. One sentence in the contract, and a habit in practice: no approval, no work.

For the first few weeks that feels bureaucratic. After that it is a routine nobody notices, and the argument about additional work disappears entirely, because every euro has a moment where you said yes.

Four things to fix in advance

What is not in the scope. That list is more useful than the scope itself, because that is where every misunderstanding starts.
How many feedback rounds are included. Rounds are the most expensive item in creative work, and they are almost never counted in a proposal.
Who may order more. If five people on your side can call the agency with a request, the scope grows by itself. One point of contact solves that.
A threshold for small things. Anything under an agreed amount goes ahead without paperwork. Without that threshold the rule becomes too heavy and nobody keeps it up.

The monthly habit

Ask for an overview of what was done that month against what was planned, on one page. Not to police it but to see deviations while they are small. An agency that cannot produce that does not know where its own hours go, and that is a bigger problem than the invoice.

And your own side of it

Late briefings, shifting feedback and decisions that come back are the most expensive things in any creative process. They do not appear on the agency's invoice, but they do get paid for.

If you want to express scope in units of work rather than in hours, that is what IKAg's PAR instrument does: a proposal converted into a number of units, with the fee beside it.