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R is called a right Pi-coherent ring in case every finitelygenerated torsionless right R-module is finitely presented. Inthis paper, we define a dimension for rings, calledPi-coherent dimension, which measures how far away a ring isfrom being Pi-coherent. This dimension has nice properties whenthe ring in question is coherent. In addition, we study someproperties of Pi-coherent rings in terms of preenvelopes andprecovers.