Approximate beta strength functions have been derived from measurements of the electroncapture beta feed to the high-lying excited states in about 40 neutron-deficient nuclei. These nuclei, available at the ISOLDE on-line facility at CERN, ranged from isotopes of iridium ( Z = 77) to those of radon ( Z = 86). The beta feed was determined from the gamma spectra by a total absorption spectrometry technique involving two 15 cm diam. × 10 cm height NaI (T1) crystals. Two sum spectra, one with and one without a coincidence demand, were recorded simultaneously for each isotope. An average multiplicity of three to four high-energy γ-rays per cascade was deduced from the ratio of these two spectra. In general, the strength functions vary smoothly with energy as well as with the neutron number N and the proton number Z. Strong peaks appear in the energy region 1.5-3.5 MeV. Relatively little strength is found below an excitation energy in the daughter nucleus corresponding approximately to the energy required for forming a (pn) pair. This overall behaviour can be understood by assuming that the main part of the strength is associated with transitions that excite protons that are initially in paired orbits. An average value overlineSβ of the beta strength function for a given isotope may be calculated if the Q-value and the gross electron-capture half-life are known. It was found that overlineSβ varies strongly but systematically with N and Z; from the light Pt isotopes with N ≈ 100 to isotopes just below the 126-neutron closed shell, it decreases by a factor of about 300. Fine structure in this dependence may be evidence for Subshell effects in deformed nuclei. The results are discussed in terms of the shell model.