An invoice goes out and the customer comes back saying it is wrong. The instinctive response, particularly if the work was good and the money is needed, is to defend the figure. That is usually a mistake, not because the figure is wrong but because the response addresses the wrong problem. A disputed invoice is not the same thing as an unpaid one. An unpaid invoice is about money or willingness; a disputed invoice is about a disagreement over what was agreed, and until that disagreement is understood, every argument about the amount is being had in the dark.
There are broadly three things that might be happening, and they call for different responses. The first is a straightforward error - a wrong quantity, a duplicated line, an old rate, a job billed twice. This is common, it is nobody's scandal, and the answer is to check, correct it and reissue quickly. The second is a genuine misunderstanding of scope: the customer believed something was included and it was not, and both parties are remembering an honest version of a conversation that was never written down. The third is a customer who does not intend to pay in full and is looking for grounds. These look similar in the first message and diverge immediately afterwards.
Distinguishing them is mostly a matter of asking rather than arguing. Ask what specifically they believe is wrong, and ask for it item by item rather than in general. A genuine error produces a specific and checkable answer. A scope misunderstanding produces a coherent account of a different expectation, usually referring to a real conversation. Someone looking for grounds tends to produce a shifting set of general complaints - the work, the timing, the manner, the price - which change when each is answered. That pattern is recognisable, and recognising it early changes what you do next.
For the first two, which are the overwhelming majority, the practical approach is the same: establish the facts quickly, concede what is genuinely yours without reluctance, explain the rest in terms of what was agreed at the time, and put a corrected invoice or a written confirmation in front of them fast. Speed matters more than people think - a dispute left open hardens as both sides mentally rehearse their case. For the third, the response is different: keep it in writing from that point on, stop doing further work, be precise and unemotional, and decide early what the matter is actually worth pursuing. And afterwards, in every case, go back and find the moment where a two-minute written confirmation would have prevented the whole thing, because in nearly every dispute that moment exists.