Spring barley (SB) (Hordeum vulgare L.) cultivar ‘Ūla’ is the most widely grown cereal in Lithuania (hereinafter LIT). Most of the SB varieties bred in LIT (‘Aidas,’ ‘Alsa,’ ‘Aura,’ and ‘Baronesse’) are suitable for growing organically. However, in contrast to conventional farming practices, they are considerably more sensitive to the organic farming conditions and lack of nitrogen required for weed suppression. One of the several organic solutions to the problem of spreading weeds lies in growing false flax (FF; Camelina sativa) as cover crop between the SB plantings. This paper aims to address two questions: 1) development of recommendations to achieve the best performance from a mixed seed drilling and 2) quantitative appraisal of the weed suppression level in mixed crop (FF+SB) against weed incidence in sole crop of SB. For this study, an experimental coulter with adjustable geometries based on a theoretical approach to characterize FF seed movement has been developed. According to laboratory test findings, three-year in-field research trials were conducted to combine both theoretical and practical aspects of integrated weed management. A series of experiments confirmed that FF could effectively limit the prevalence of weeds under certain soil properties and weather conditions typical to LIT. The main conclusion was that drilling FF in strips between SB rows reduced the amount of weeds by 1.79 times in relation to “no-FF” practices without a significant decrease in SB yield. The proposed weed management strategy is effective, reliable, practical, and economical.