Introduction: People who experience non-affective psychosis are particularly vulnerable to death by suicide. Psychological talking therapies can alleviate suicidal thoughts, plans, and attempts. Therapies need to be effective, but also acceptable, to recipients and those delivering them. We used the Theoretical Framework of Acceptability (TFA) to investigate individuals' views on the acceptability of a theoretically grounded suicide-focused cognitive therapy for people experiencing psychosis (i.e., CBSPp). The therapy was developed by our team, in the context of a randomised controlled trial (RCT) as part of the CARMS (Cognitive AppRoaches to coMbatting Suicidality) project. Methods: Individuals with both non-affective psychosis and recent suicidal thoughts, plans and/or attempts were recruited from NHS community mental health services across NW England, UK. Qualitative interviews were conducted with participants who were randomised to receive therapy as part of the RCT. All interviews were audio-recorded and transcribed verbatim with participants’ consent. Data were deductively analysed using an adapted version of the Theoretical Framework of Acceptability, and inductively analysed using thematic analysis. An expert by experience group of individuals with experiences of psychosis and suicidality was involved in the study design and dissemination. Results: Interviews were conducted with 21 participants. The mean interview length was 45 minutes. Data were organised into six themes: 1. Affective attitude, 2. Burden, 3. Alliance, 4. Intervention coherence, 5. Perceived effectiveness, and 6. Self-efficacy. No evidence was found for two of the original TFA themes, namely Ethicality and Opportunity costs. There was strong evidence for the Affective attitude and Alliance themes. Overall, our suicide-focused therapy was perceived as being acceptable and beneficial for well-being and understanding experiences of suicidality and psychosis. Conclusions: Talking about experiences of suicide was difficult and sometimes distressing. However, it was perceived to be useful for understanding mental health experiences. In order for an intervention to be acceptable, therapists need to ensure that clients' understanding of the therapy aims aligns with expectations of effectiveness. It is also important for stakeholders to invest in building strong therapeutic relationships. Future research will benefit from examining therapists' experiences of delivering therapy through different modes, such as online and telephone.