After some introductory and partly critical considerations about fundamental trust - as it is conceived by the Danish phenomenologist K. E. Løgstrup in his ‘Analysis of trust' in the first section of his work The Ethical Demand - this paper explores two ways of constituting what I call non-fundamental trust. For this purpose I work with two examples. The first one concerns a rather passive constitution of non-fundamental trust bound up with perception, the other one concerns a rather active constitution of non-fundamental trust bound up with imaginative intentionality. Both examples have their source of inspiration in phenomenological philosophers, namely Maurice Merleau-Ponty and Jean-Paul Sartre. As an intermezzo I reflect upon the experience of a compromised personal freedom, which I consider in relation to the examples that I give and to our conference theme, ‘trusting the new', as well.