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In this paper we report an analysis of the physical phenomena that can affect the frequency stability of optically pumped vapor cell clocks working in pulsed regime. It is well known that the pulsed approach allows a strong reduction of the light shift that is one of the main sources of frequency instability. However, other instability sources can degrade clock performance by limiting both short- and medium-term frequency stability. After recognizing the different noise sources and realizing how they are transferred to the clock transition, we propose some technical solutions to limit their effects, extending the region of white frequency noise up to integration times τ of the order of 104 s.