Fe/MgB2 tapes have been prepared starting with pre-reacted binary MgB2 powders. As shown by resistive and inductive measurements, the reduction of particle size to a few microns by ball milling has little influence on Bc2, while the superconducting properties of the individual MgB2 grains are essentially unchanged. Reducing the particle size causes an enhancement of Birr from 14 to 16 T, while Jc has considerably increased at high fields, its slope Jc(B) being reduced. At 4.2 K, values of 5.3 × 104 and 1.2 × 103 A/cm2 were measured at 3.5 and 10 T, respectively, suggesting a dominant role of the conditions at the grain interfaces. A systematic variation of these conditions at the interfaces is undertaken in order to determine the limit of transport properties for Fe/MgB2 tapes. The addition of 5% Mg to MgB2 powder was found to affect neither Jc nor Bc2. For the tapes with the highest Jc values, very high exponential n factors were measured: n=148, 89 and 17 at 3.5, 5 and 10 T, respectively and measurements of critical current versus applied strain have been performed. The mechanism leading to high transport critical current densities of filamentary Fe/MgB2 tapes based on MgB2 particles is discussed.