WASHINGTON — FIFTY years ago, in Gideon v. Wainwright, the Supreme Court ruled that poor people accused of serious crimes were entitled to lawyers paid for by the government. But the court did not say how the lawyers should be chosen, how much they should be paid or how to make sure they defended their clients with vigor and care.

This created a simple problem and a complicated one. The simple one is that many appointed lawyers are not paid enough to allow them to do their jobs. The solution to that problem is money.

The complicated problem is that the Gideon decision created attorney-client relationships barely worthy of the name, between lawyers with conflicting incentives and clients without choices. Now a judge in Washington State and a county in Texas are trying to address that deeper problem in ways that have never been tried in the United States.

Their proposed solutions reflect competing schools of legal thought. The approach in Washington State is a top-down exercise of federal power, pushing lawyers to make sure they meet with their clients, tell them their rights, investigate their cases and represent them zealously in plea negotiations and at trial.