Summary: In this note we study interpolants to \(n\)-variate, real-valued functions from radial function spaces, i.e., spaces that are spanned by radially symmetric functions \(\varphi(|\cdot- x_j|_2)\) defined on \(\mathbb{R}^n\). Here \(|\cdot|_2\) denotes the Euclidean norm, \(\varphi: \mathbb{R}_+\to \mathbb{R}\) is a given “radial (basis) function” which we take here to be \(\varphi(r)= (r^2+ c^2)^{\beta/2}\), \(- n\leq \beta< 0\), and the \(\{x_j\}\subset \mathbb{R}^n\) are prescribed “centres”, or knots. We analyze the effect of removing a knot from a given interpolant, in order that in applications one can see how many knots can be eliminated from an interpolant so that the interpolant remains within a given tolerance from the original one.