A detailed discussion is given of the analysis of recent data to obtain improved upper bounds on the couplings $|U_{e4}|^2$ and $|U_{mu 4}|^2$ for a mainly sterile neutrino mass eigenstate $ u_4$. Using the excellent agreement among ${cal F}t$ values for superallowed nuclear beta decay, an improved upper limit is derived for emission of a $ u_4$. The agreement of the ratios of branching ratios $R^{(pi)}_{e/mu}=BR(pi^+ to e^+ u_e)/BR(pi^+ to mu^+ u_mu)$, $R^{(K)}_{e/mu}$, $R^{(D_s)}_{e/tau}$, $R^{(D_s)}_{mu/tau}$, and $R^{(D)}_{e/tau}$, and the branching ratios $BR(B^+rightarrow e^+ u_e)$ and $BR(B^+rightarrow mu^+ u_mu)$ decays with predictions of the Standard Model, is utilized to derive new constraints on $ u_4$ emission covering the $ u_4$ mass range from MeV to GeV. We also discuss constraints from peak search experiments probing for emission of a $ u_4$ via lepton mixing, as well as constraints from pion beta decay, CKM unitarity, $mu$ decay, leptonic $tau$ decay, and other experimental inputs.
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