Elastic ethylene polymers are disclosed which have processability similar to highly branched low density polyethylene (LDPE), but the strength and toughness of linear low density polyethylene (LDPE). The polymers have processing indices (PI's) less than or equal to 70 percent of those of a comparative linear ethylene polymer and a critical shear rate at onset of surface melt fracture of at least 50 percent greater than the critical shear rate at the onset of surface melt fracture of a traditional linear ethylene polymer at about the same I2and Mw/Mn. The novel polymers can also have from about 0.01 to about 3 long chain branches/1000 total carbons and have higher low/zero shear viscosity and lower high shear viscosity than comparative linear ethylene polymers. The novel polymers can also be characterized as having a melt flow ratio, I10/I2, ≧5.63, a molecular weight distribution, Mw/Mn, defined by the equation: Mw/Mn≦(I10/I2)−4.63, a critical shear stress at onset of gross melt fracture greater than about 4×106 dyne/cm2, and a single DSC melt peak between −30 C and 150 C.