the relation $\tau a=a^q\tau$ for all $a\in K$. A *Drinfeld $A$-module* (of generic characteristic) over $K$ is a homomorphism of ${{\mathbb{F}}}_q$-algebras $$\psi\colon A\to K[\tau],\,\,a\mapsto \psi_{a,0}+\psi_{a,1}\tau+\psi_{a,2}\tau^2+\ldots$$ such that $\psi_{a,0}=a$ for all $a\in A$, and $\psi(A)\not\subset K.$

Let $\psi$ be a Drinfeld $A$-module over $K$. There exists an $n\in{{\mathbb{Z}}}_{>0}$ such that $\deg_\tau(\psi_a)=n\deg_A (a)$ for all $a\in A$, where $\deg_A (a):=\dim_{{{\mathbb{F}}}_q}A/(a).$ The integer $n$ is called the *rank* of $\psi.$ Let $I\subset A$ be a non-zero proper ideal. A *level $I$ structure* on $\psi$ is an $A$-module isomorphism $$\lambda\colon(I^{-1}A/A)^r\stackrel\sim\longto\bigcap_{i\in I}\ker(\psi_i)=:\psi[I]\subset K.$$ Here $\ker(\psi_i)$ denotes the set of zeros of $\psi_i$ (a priori contained in an algebraic closure of $K$), and the definition of $\lambda$ presupposes that $\psi[I]\subset K$.

One can generalize these notions and define Drinfeld $A$-modules of rank $n$ and level $I$ over an arbitary $F$-scheme. The corresponding moduli functor is represented by a smooth irreducible $(n-1)$-dimensional affine algebraic variety $M^n_{A,I}$ over $F$. It is then natural to search for meaningful compactifications of $M^n_{A,I}$. An example is the *Satake compactification* of Pink [@Pink], which he denotes by $\overline{M}^n_{A,I}$. This is normal integral proper algebraic variety over $F$, but is singular when $n\geq 3$ (see [@Pink Theorem 7.8]). It is our hope that 