A glass cuboid, embedded inside a dielectric cylinder is studied when illuminated with a monochromatic plane wave. A photonic nanojet (PNJ) with a full-width at half-maximum (FWHM) waist of around 0.25λ0 is obtained outside the external surface of the cuboid. The influence of the parameters of a square section cuboid is studied. Three particular phenomena can be obtained and are discussed: an ultra-narrow PNJ on the external surface of the cuboid, a long photonic jet and the excitation of whispering gallery modes (WGMs). A parametric study, over the width and the height of a rectangular section cuboid, shows that these parameters can be used to control the photonic jet properties. We also study several other geometries of the insert, which shows that the key parameter is the refractive index of the inserted material. Finally, we show that by changing the incident angle we can obtain a curved photonic jet.