D.C. MAYOR Muriel E. Bowser (D) had cause to take pride in a recent groundbreaking for the first of six family homeless shelters set to replace the decrepit facility at the former D.C. General Hospital. Unlike previous mayors with similar plans, Ms. Bowser was able to overcome neighborhood opposition, personal attacks and other obstacles.

The tragic disappearance three years ago of 8-year-old Relisha Rudd from D.C. General followed years of official tolerance of children and their families being housed in intolerable conditions. Relisha, missing and presumed dead, slipped through the safety net of city services and workers that was supposed to help her. She was last seen in the company of a janitor who worked at D.C. General and who killed himself while being investigated in Relisha’s disappearance.

Ms. Bowser campaigned on a pledge to close D.C. General, which started in 2001 as an overflow winter shelter but soon became a year-round shelter and currently houses 270 families. The groundbreaking at an empty office building in Ward 4 that is being retrofitted to house 45 homeless families brings the city one step closer to shutting down the decaying and bug-ridden behemoth. Work is set to begin soon on shelters in Wards 7 and 8 and in the coming months in Wards 3, 5 and 6. The small size of the replacement shelters — “beautiful and dignified places” is how Ms. Bowser once described them — is seen as a more effective environment in which to tackle the combination of issues that result in homelessness.

The administration had hoped to close D.C. General by 2018, but changes by the D.C. Council to the mayor’s original plan and fierce neighborhood opposition, including lawsuits in Wards 3 and 5, have pushed that back at least a year. As the replacement shelters are brought online and families move out of D.C. General, it is important that the city, which also rents motel rooms to house homeless families, not fall into the trap of refilling the rooms.

Good, then, to hear Ms. Bowser promise that her plans — and her resolve — include not just emptying D.C. General but tearing it down.