As the demand for the transmission of electric power and communication signals in automotive and aerospace vehicles increases, so does the number of structures comprising simplified one-dimensional attachments, such as electrical cabling, affixed to a host plate like primary structure. These attachments are typically uncertain in their geometric or material properties, potentially affecting the response of the built-up structure. Difficulties then arise in the prediction of the response of the assembly. This study shows how the variability, due to the uncertain attachments, might be reduced by considering flexible connections. A mobility analysis compares systems connected with either rigid links or elastic springs. A frequency is identified at which the assembly dynamically uncouples; the effect on the host response variability due to the uncertain attachment decreases above this frequency with a reduction of the order of 60 dB in the coefficient of variation. This uncoupling or effective isolation frequency can be simply estimated from the mobility of the elastic connection and the properties of the nominal structural attachment. For design purposes, this frequency can be adjusted to achieve a more predictable response above a given frequency.