**Non-central polynomial potentials in two dimensions are considered.****Their unbounded decrease causing an accelerated escape of classical particles in some directions is admitted.****We show that quantization prevents such an "explosion" below a certain critical strength of repulsion.****An analogy with the well known fall of particles in a "too attractive" singularity is emphasized.**

**You may click on the ps formatted****full text,****figure 1****and****figure 2.****as published in****J. Phys. A: Math. Gen. 31 (1998) 3349 - 3355.**