It is well known that the downsizing philosophy allows the improvement of the brake specific fuel consumption (BSFC) at part load operation for spark ignition (SI) engines. On the other hand, the BSFC is penalized at high load because of the knock occurrence and of further limitations on the turbine inlet temperature (TIT). Knock control forces the adoption of a late combustion phasing, causing a deterioration of the thermodynamic efficiency, while the TIT control requires the enrichment of the air-to-fuel ratio (A/F), with additional BSFC drawbacks. In this work, two promising techniques are investigated by a 1D approach with the aim of improving the fuel economy of a turbocharged SI engine at full load knock-limited operation. The first technique is the recirculation of low-pressure cooled exhaust gas (EGR), while the second is the injection of liquid water at the intake ports. Proper "in-house developed" sub-models are used to describe the turbulence, combustion and knock phenomena. The effects of the above techniques are studied in six operating points at full load and different speeds for various A/F levels and inert content, by varying the EGR rate and water-to-fuel ratio. The presented results highlight that both the solutions involve significant BSFC improvements, especially in the operating conditions at medium engine speeds. In fact, the introduction of inert gas in the cylinder contributes to reduce the knock tendency, resulting in the possibility to advance the combustion phasing and reduce, or even avoid, the mixture over-fuelling. The heat subtracted by the water evaporation enhances the above effects, resulting in an improved fuel economy. However, the BSFC advantages are limited by the maximum allowable in-cylinder pressure, TIT, turbocharger speed, and boost level. The developed numerical procedure is able to take into account the complex interactions among different driving parameters affecting the engine behaviour. It can be hence very useful to define a numerical engine pre-calibration and to realistically predict the EGR- and water injection-related BSFC advantages. (C) 2016 Elsevier Ltd. All rights reserved.