Two impact modifiers, based respectively on polybutadiene (PB) and poly(butyl acrylate-co-styrene) (PBA), are compared in blends with four glassy polymers: polycarbonate (PC), poly(methyl methacrylate) (PMMA), poly(styrene-co-acrylonitrile) (PSAN), and poly(vinyl chloride) (PVC). Dynamic mechanical tests show glass transitions at about -80 °C in PB and -15 °C in PBA. Both modifiers have grafted PMMA shells, which are seen in the transmission electron microscope (TEM) to be about 10 nm thick. The two-stage PB particles have 200-nm-diameter polybutadiene cores, whereas the three-stage PBA particles have 260-nm-diameter PMMA cores, with 20-nm thick PBA rubber inner shells. Under tension, the PB particles cavitate to form single voids on reaching a critical volume strain, and subsequently offer little resistance to dilatation. By contrast, tensile tests performed in situ in the TEM show that the PBA shells form fibrils that are anchored to the rigid core, and act as constraints on further dilatation: the stresses developed in the PBA fibrils can be sufficient to draw fibrils from both the PMMA core and the PSAN matrix. There is evidence that the PMMA shells can debond from the matrix both in cryogenic fracture and in fatigue at 23 °C. Tensile dilatometry shows that the PB particles cavitate at higher strains than the PBA particles, but that the PB particles then cause a rapid volume increase, leading to a low strain at break. By contrast, the PBA particles produce a more controlled dilatation, and higher strains to break. Later papers in this series treat the mechanical and rheological behavior of these blends in more detail.