This paper presents results from a study of propagation of very-low-frequency electromagnetic waves (whistlers) inside high-density ducts (HDDs) in the Earth's magnetosphere. The main hypothesis investigated in this study is that whistlers can propagate without any attenuation inside HDD when the width of the duct channel is equal to the integer number of perpendicular wavelengths of the waves inside the duct. This condition provides a simple and efficient procedure to determine nonleaking eigenmodes of HDDs. Our analysis of this nonleaking condition reveals several new and important properties of HDDs which were never discussed before. In particular, this condition shows that any HDD has only a finite number of nonleaking eigenmodes. This number is proportional to the width of the duct and the magnitude of the plasma density inside the duct. Thus each value of the density inside the duct defines minimum width of the duct channel providing the nonleaking ducting, and each width of the duct channel defines a minimal density magnitude providing the nonleaking ducting. HDDs with the same value of the product of the duct width times the square root of the plasma density have the same number of nonleaking eigenmodes and frequencies of the corresponding eigenmodes are the same. A broader (or with higher density) HDD can guide without leakage whistlers with higher frequencies than a narrower (or with lower density) HDD.