Involvement of parents and teachers into decision making about evaluation criteria allows to establish partnership relations, confidence and awareness in implementation of preschool education programs. Such dialogue is necessary at the stage of transition to new norm, implementation of new national standards. In order to reveal the concepts of teachers and parents about good kindergarten, the research was carried out (anonymous survey using standard toolkit of European Quality Seal international project). The participants were 57 teachers and 284 parents from 26 Moscow schools with full-day preschool groups. The point of view of 18 experts in the field of preschool education was presented additionally. In general, the proposed criteria are important for respondents of all categories. Teachers demonstrate higher mean values in comparison with parents. Teachers and parents often have the same concepts about the value of these or those provisions: participation of parents in learning process as well as fee from parents are not important. Child-adult interaction, child’s well-being and safety are the main priorities. The experts partially agree with teachers and parents concerning the most and the least significant criteria: among the most important, together with well-being, individualization of education and free play time are highlighted. The survey results can provide an objective ground for dialogue between teachers, parents, and authorities both at the level of ECEC service and at municipal, regional, and federal education system levels.