The problem is that "immigrants" is an extremely imprecise category. I don't know enough about Sweden, but I know that in Germany, foreign crime is primarily do

The problem is that "immigrants" is an extremely imprecise category. I don't know enough about Sweden, but I know that in Germany, foreign crime is primarily dominated by organized crime from abroad: pickpocket gangs from North Africa, burglary gangs from Serbia and Georgia, the Russian Mafia, Lebanese crime clans, etc. In contrast, Syrian refugees seem to be among the most law-abiding foreigners you can find (followed by Iraqi refugees, as I recall). "Immigrants" is a fairly useless category for criminological purposes, as it combines several other categories with vastly different profiles, some with outsized crime rates, some below that of natives.