An axi-centrifugal compressor for a gas turbine propulsion system for an aircraft comprising: a housing; and a compressor rotatably supported on a shaft assembly in the housing and operable to effect a pressure ratio along a flow path between a compressor inlet and a compressor exit; wherein the compressor includes: an axial compressor section having at least one axial stage operable to effect a first pressure ratio along the flow path between the compressor inlet and a first section exit; a centrifugal compressor section operable to effect a second pressure ratio along the flow path between a second section inlet and the compressor exit, wherein the first section exit associated with the axial compressor section leads directly into the second section inlet associated with the centrifugal section along the flow path; wherein the compressor has a tuning factor satisfying the following condition over the range of expected operating conditions: 2.8 < PR ax / PR c < 4.5 where: PR ax is the first pressure ratio, and PR c is the second pressure ratio; and a loading factor satisfying the following condition over the range of expected operating conditions: 0.6 < PR ax 1 n / PR c < 0.8 where: n is the number of axial stages in the axial compressor section, and wherein: the axial compressor section comprises a plurality of axial stages (122.1; 122.2; 122.3) in the axial compressor section; each of the plurality of axial stages comprises at least one stator assembly (190; 192; 194; 196) and a rotor assembly (200; 202; 204) operably coupled to the shaft assembly for rotation relative to the stator assembly; the plurality of rotor assemblies are coupled for co-rotation on the shaft assembly; the shaft assembly operably couples the axial compressor section and the centrifugal compressor section for co-rotation thereon; and the plurality of axial stages are coupled for co-rotation with the centrifugal compressor section. a housing; and a compressor rotatably supported on a shaft assembly in the housing and operable to effect a pressure ratio along a flow path between a compressor inlet and a compressor exit; wherein the compressor includes: an axial compressor section having at least one axial stage operable to effect a first pressure ratio along the flow path between the compressor inlet and a first section exit; a centrifugal compressor section operable to effect a second pressure ratio along the flow path between a second section inlet and the compressor exit, wherein the first section exit associated with the axial compressor section leads directly into the second section inlet associated with the centrifugal section along the flow path; wherein the compressor has a tuning factor satisfying the following condition over the range of expected operating conditions: 2.8 < PR ax / PR c < 4.5 where: PR ax is the first pressure ratio, and PR c is the second pressure ratio; and a loading factor satisfying the following condition over the range of expected operating conditions: 0.6 < PR ax 1 n / PR c < 0.8 where: n is the number of axial stages in the axial compressor section, and wherein: the axial compressor section comprises a plurality of axial stages (122.1; 122.2; 122.3) in the axial compressor section; each of the plurality of axial stages comprises at least one stator assembly (190; 192; 194; 196) and a rotor assembly (200; 202; 204) operably coupled to the shaft assembly for rotation relative to the stator assembly; the plurality of rotor assemblies are coupled for co-rotation on the shaft assembly; the shaft assembly operably couples the axial compressor section and the centrifugal compressor section for co-rotation thereon; and the plurality of axial stages are coupled for co-rotation with the centrifugal compressor section. an axial compressor section having at least one axial stage operable to effect a first pressure ratio along the flow path between the compressor inlet and a first section exit; a centrifugal compressor section operable to effect a second pressure ratio along the flow path between a second section inlet and the compressor exit, wherein the first section exit associated with the axial compressor section leads directly into the second section inlet associated with the centrifugal section along the flow path; wherein the compressor has a tuning factor satisfying the following condition over the range of expected operating conditions: 2.8 < PR ax / PR c < 4.5 where: PR ax is the first pressure ratio, and PR c is the second pressure ratio; PR ax is the first pressure ratio, and PR c is the second pressure ratio; and a loading factor satisfying the following condition over the range of expected operating conditions: 0.6 < PR ax 1 n / PR c < 0.8 the axial compressor section comprises a plurality of axial stages (122.1; 122.2; 122.3) in the axial compressor section; each of the plurality of axial stages comprises at least one stator assembly (190; 192; 194; 196) and a rotor assembly (200; 202; 204) operably coupled to the shaft assembly for rotation relative to the stator assembly; the plurality of rotor assemblies are coupled for co-rotation on the shaft assembly; the shaft assembly operably couples the axial compressor section and the centrifugal compressor section for co-rotation thereon; and the plurality of axial stages are coupled for co-rotation with the centrifugal compressor section.