Models for glacial isostatic adjustment (GIA) can provide constraints on rheology of the mantle if past ice thickness variations are assumed to be known. The Pleistocene ice loading histories that are used to obtain such constraints are based on an a priori 1-D mantle viscosity profile that assumes a single deformation mechanism for mantle rocks. Such a simplified viscosity profile makes it hard to compare the inferred mantle rheology to inferences from seismology and laboratory experiments. It is unknown what constraints GIA observations can provide on more realistic mantle rheology with an ice history that is not based on an a priori mantle viscosity profile. This paper investigates a model for GIA with a new ice history for Fennoscandia that is constrained by palaeoclimate proxies and glacial sediments. Diffusion and dislocation creep flow law data are taken from a compilation of laboratory measurements on olivine. Upper-mantle temperature data sets down to 400 km depth are derived from surface heatflow measurements, a petrochemical model for Fennoscandia and seismic velocity anomalies. Creep parameters below 400 km are taken from an earlier study and are only varying with depth. The olivine grain size and water content (a wet state, or a dry state) are used as free parameters. The solid Earth response is computed with a global spherical 3-D finite-element model for an incompressible, self-gravitating Earth. We compare predictions to sea level data and GPS uplift rates in Fennoscandia. The objective is to see if the mantle rheology and the ice model is consistent with GIA observations. We also test if the inclusion of dislocation creep gives any improvements over predictions with diffusion creep only, and whether the laterally varying temperatures result in an improved fit compared to a widely used 1-D viscosity profile (VM2). We find that sea level data can be explained with our ice model and with information on mantle rheology from laboratory experiments, heatflow and seismology and a pure olivine rheology above 400 km. Moreover, laterally heterogeneous models provide a significantly better fit to relative sea level data than the VM2 viscosity, for our ice model as well as for the ICE-5G model that is based on the VM2 profile. The new ice model gives different constraints on mantle rheology than the ICE-5G model, indicating a possible bias towards mantle viscosity in the latter or shortcomings in our ice model. Present-day uplift rates for a dry rheology are close to GPS observed uplift rate for certain combinations of grain size and temperature fields. Sea level data show a preference for a wet olivine rheology, but in that case uplift rates are too low for all grain sizes and temperature fields. The difficulty to fit sea level data and uplift rate data simultaneously can not be resolved by varying creep parameters below 400 km. Uncertainties in the flow law and the neglect of other materials in the upper mantle, as well as the neglect of flow in the crust could affect our conclusions.