This paper investigates citizens' counter-strategies to the use of Artificial Intelligence (AI) by law enforcement agencies (LEAs). Based on information from three countries (Greece, Italy and Spain) we demonstrate disparities in the likelihood of ten specific counter-strategies. We further identified factors that increase the propensity for counter-strategies. Our study provides an important new perspective to societal impacts of security-focused AI applications by illustrating the conscious, strategic choices by citizens when confronted with AI capabilities for LEAs.