Wales Opens First Drug Court
Speaking about the Cardiff court, he said: "Drug-related crime can have a devastating effect on communities.
"Offenders often become caught up in a cycle of crime to fuel their habits, which in turn means their local community is blighted.
"It is vital we find new and innovative ways of tackling this - our ultimate goal is to reduce re-offending and make Cardiff a safer place to live.
Mr Straw said offenders came from "chaotic backgrounds" where stability was lacking, so continuity in the court was especially important.
"The idea is that seeing familiar faces can help build a relationship between the judge and addict, motivating offenders to salvage their life from the hold of drugs," he added.
"When the cycle of drug abuse and crime is broken, and someone changes their life for the better, the whole community benefits."
Three other drug courts have also opened in Barnsley, Salford and Bristol magistrates' courts.