Clients often ask me to apply for variances to increase the height of the roof, or to build closer to the property line than allowed. These are almost never approved, but there are exceptions.
One recent example in my office: a 1920s mansion in Hancock Park. The detached garage had servants' quarters on the second floor. The owners wanted to legalize the apartment’s status, and offer it as a rental. The code allows this use, so long as the structure complies with the same property-line setbacks that apply to the main house.
The problem: the garage/apartment was too close to the side property line (by six inches), and did not comply with the current zoning code. If we could find an old building permit that included the guest quarters over the garage, we’d be home free: in that case the City would likely approve the project (subject to a yard reduction application and neighbors’ approval), since it complied with the zoning code when it was originally built.
We conducted a permit search and found, in the city’s microfilm records, a 1927 permit for the garage and servants’ quarters above. This made it possible to legalize the unit with a form of variance (applying for a yard reduction), even though it didn’t comply with the current zoning code.

Many variances never get approved, except in special circumstances
In most cases the Los Angeles Department of Building and Safety rarely approves variances for single-family residential projects. Applications are almost never approved–unless there is an unusual condition with the property that makes it impossible to comply with the building or zoning code without a variance, or in cases where the impact to neighbors is minimal.
Going through the variance process can be costly, lengthy (often six to ten months), and is normally unlikely to succeed, except for exceptions.
Certain minor variances are often approved with certain conditions (minor encroachments into side-yards, for example, as long as there’s a credible reason and neighbors approve). As for larger variances–it’s worth studying those situations closely with the help of a Building and Safety official before developing a design, to get an idea of the likelihood of success. The City of Los Angeles provides preliminary plan-check consultations for these purposes, and I’ll describe those in another post.