The U.S. Army has high standards, but frequently makes exceptions if recruiters believe the recruit has other qualities that will compensate for some shortcomings. Thus the recruiting commanders can get some standards waived, up to a point, for 10-15 percent of their prospects each year. In 2005, 15 percent of recruits got in on waivers, up from 12 percent in 2004. That's an increase, in 2005, of 1,700 waivers granted.
The most common items waived are medical conditions, criminal records or drug use. For example, many urban recruits have asthma problems. If the recruit is headed for a job that does not require the kind of physical effort that low grade asthma would interfere with, a waiver would be granted. If a prospect has a low grade (no felonies) criminal record, and appears to have moved on from that sort of thing, a waiver is possible. Same with prior drug use. Prospects are made aware of the regular, unannounced, drug tests for troops on active duty.
The army has long used statistical analysis of recruit records, and the subsequent performance of those soldiers. From that it is known that recruits with physical or psychological problems are harder, and often impossible, to train. Those with criminal tendencies are often disciplinary problems, even after training, and many of these have to be discharged before their term of service is up. However, after studying millions of recruits, the army has refined its parameters for what kind of person will make a successful soldier. So waivers are not as risky as they used to be. But there is always risk, and greater cost. "Waiver recruits" are more expensive to train, and many of them get tossed out later. But the majority do well. So if you want more troops, you can take chances on more "waiver recruits." It will be more expensive, and cause more headaches for NCOs and officers that have to deal with them, but it's a way to keep your numbers up.