As we increase the scale of superconducting quantum-computing circuits, we face challenges in maintaining high-fidelity quantum gates across the device. Fixed-frequency tansmons offer excellent coherence, noise stability and simplicity of operation, making them an ideal qubit platform for large-scale circuits. However, established fabrication methods cannot set the frequencies of such qubits with precision better than about 2%. High two-qubit gate fidelities require precise control of the relative qubit frequencies. To quantify the precision needed, we define “frequency collisions” in a cross-resonance gate architecture, and show statistically that 2% frequency precision is insufficient to evade such collisions. To overcome this challenge, we introduce a ‘heavy hexagon’ lattice of qubits along with selective laser-anneal to tune the qubits into desired frequency patterns. This anneal procedure offers a nearly tenfold improvement in qubit frequency precision. In 28-qubit and 65-qubit processors, we demonstrate no measurable effect of this tuning on qubit coherence, and median two-qubit gate fidelity of 98.7%. We discuss the application of these techniques to the current generation of processors at 100-qubit scale, as well as prospects for further scaling. Precise control of qubit frequencies will be essential to increasing quantum volume and to achieving quantum advantage, at the 1000 qubit scale and beyond.