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[Abridged] I report the discovery of modulations in radial velocity (RV)curves of four Galactic classical Cepheids and investigate their impact as asystematic uncertainty for Baade-Wesselink distances. Highly precise Dopplermeasurements were obtained using the Coralie high-resolution spectrograph since2011. Particular care was taken to sample all phase points in order to veryaccurately trace the RV curve during multiple epochs and to search fordifferences in linear radius variations derived from observations obtained atdifferent epochs. Different timescales are sampled, ranging from cycle-to-cycleto months and years. The unprecedented combination of excellent phase coverageobtained during multiple epochs and high precision enabled the discovery ofsignificant modulation in the RV curves of the short-period s-Cepheids QZNormae and V335 Puppis, as well as the long-period fundamental mode Cepheids lCarinae and RS Puppis. The modulations manifest as shape and amplitudevariations that vary smoothly on timescales of years for short-period Cepheidsand from one pulsation cycle to the next in the long-period Cepheids. The orderof magnitude of the effect ranges from several hundred m/s to a few km/s. Theresulting difference among linear radius variations derived using data fromdifferent epochs can lead to systematic errors of up to 15% forBaade-Wesselink-type distances, if the employed angular and linear radiusvariations are not determined contemporaneously. The different natures of theCepheids exhibiting modulation in their RV curves suggests that this phenomenonis common. The observational baseline is not yet sufficient to conclude whetherthese modulations are periodic. To ensure the accuracy of Baade-Wesselinkdistances, angular and linear radius variations should always be determinedcontemporaneously.

Tuning in on Cepheids: Radial velocity amplitude modulations. A source of systematic uncertainty for Baade-Wesselink distances