diff --git a/Hlt/RecoConf/python/RecoConf/hlt2_global_reco.py b/Hlt/RecoConf/python/RecoConf/hlt2_global_reco.py
index f8b51bb3ac27663c0b0892169e979e4419a8585e..f6711315b31770dc7a174ac93431c43489e6272a 100644
--- a/Hlt/RecoConf/python/RecoConf/hlt2_global_reco.py
+++ b/Hlt/RecoConf/python/RecoConf/hlt2_global_reco.py
@@ -69,7 +69,7 @@ def make_reconstruction(light_reco=True,
             tracks=tracks_v3, track_types=rich_and_charged_proto_track_types)
         muon_pids, muon_tracks = make_conv_muon_pids(
             muonRecConfs,
-            persisted_tracks,
+            tracks_rels,
             track_types=rich_and_charged_proto_track_types)
 
     # RICH
@@ -107,8 +107,8 @@ def make_reconstruction(light_reco=True,
     ####
     output = {
         "AllTrackHandles": hlt2_tracks,
-        "VeloTracks": persisted_tracks['UnfittedVelo'],
-        "Ttracks": persisted_tracks['UnfittedTtrack'],
+        "VeloTracks": persisted_tracks['Velo'],
+        "Ttracks": persisted_tracks['Ttrack'],
         "PVs": pvs["v3"],
         "PVs_v1": pvs["v1"],
         "NeutralProtos": neutral_protos['ProtoParticleLocation'],
diff --git a/Hlt/RecoConf/python/RecoConf/hlt2_probetracks.py b/Hlt/RecoConf/python/RecoConf/hlt2_probetracks.py
index bb0f6d73a27744e2ed20eb8ddfdd5b9387c5aabe..0741b1935c415d8f1cbe37d716017fe7c4f60016 100644
--- a/Hlt/RecoConf/python/RecoConf/hlt2_probetracks.py
+++ b/Hlt/RecoConf/python/RecoConf/hlt2_probetracks.py
@@ -25,7 +25,7 @@ from PyConf.Tools import (
     ChargedProtoParticleAddMuonInfo,
 )
 from .hlt1_muonid import make_muon_hits
-from .muon_reconstruction import make_all_muon_pids, make_conv_muon_pids, make_muon_input_tracks
+from .muon_reconstruction import make_all_muon_pids, make_conv_muon_pids
 from .hlt1_tracking import (
     make_hlt1_tracks,
     get_track_master_fitter,
@@ -38,7 +38,7 @@ from .hlt1_tracking import (
 from .hlt2_tracking import (
     make_seeding_tracks, make_PrLongLivedTracking_tracks,
     make_PrHybridSeeding_tracks, get_UpgradeGhostId_tool,
-    make_hlt2_tracks_without_UT)
+    make_hlt2_tracks_without_UT, convert_tracks_to_v3_from_v1)
 
 
 @configurable
@@ -90,15 +90,14 @@ def make_charged_downstream():
         AddGhostProb=True,
         FitTracks=False).TracksOutContainer
 
-    muon_input_tracks = make_muon_input_tracks(
-        best_tracks, light_reco=False, track_types=['Downstream'])
+    tracks_v3, tracks_rels = convert_tracks_to_v3_from_v1({
+        'Downstream':
+        best_tracks['v1']
+    })
+
     muonRecConfs = make_all_muon_pids(
-        tracks=muon_input_tracks, track_types=['Downstream'])
-    muon_pids, muon_tracks = make_conv_muon_pids(
-        muonRecConfs,
-        best_tracks,
-        light_reco=False,
-        track_types=['Downstream'])
+        tracks=tracks_v3, track_types=['Downstream'])
+    muon_pids, muon_tracks = make_conv_muon_pids(muonRecConfs, tracks_rels)
     addInfo = [
         ChargedProtoParticleAddMuonInfo(
             name='addMuonInfo', InputMuonPIDLocation=muon_pids['Downstream'])
diff --git a/Hlt/RecoConf/python/RecoConf/hlt2_tracking.py b/Hlt/RecoConf/python/RecoConf/hlt2_tracking.py
index edbc8de326c38cc563cf22a6bcd98dd48787561d..86fc01e695e0cb3595dfc633464eb34a31e70d4a 100644
--- a/Hlt/RecoConf/python/RecoConf/hlt2_tracking.py
+++ b/Hlt/RecoConf/python/RecoConf/hlt2_tracking.py
@@ -1507,11 +1507,11 @@ def get_persisted_tracks_per_type(hlt2_tracks, persist=True):
             'key': 'BestUpstream',
             'location': 'UpstreamTracks'
         },
-        'UnfittedTtrack': {
+        'Ttrack': {
             'key': 'SeedDecloned',
             'location': 'Ttracks'
         },
-        'UnfittedVelo': {
+        'Velo': {
             'key': 'Velo',
             'location': 'VeloTracks'
         },
@@ -1524,14 +1524,15 @@ def get_persisted_tracks_per_type(hlt2_tracks, persist=True):
             # of them (but needs this type to be persistable) or set at moment of producing
             in_tracks = hlt2_tracks[config['key']]['v1']
             tracks[track_type] = TrackContainersMerger(
-                name=f"CreateBest{track_type}Container" + "_{hash}",
+                name=f"Persistable{track_type}TracksContainer" + "_{hash}",
                 InputLocations=[in_tracks],
                 outputs={
                     'OutputLocation': persistable_location(config['location'])
                 }).OutputLocation if persist else in_tracks
         else:
             tracks[track_type] = TracksEmptyProducer(
-                name=f"TracksEmptyProducer_{track_type}" + "_{hash}",
+                name=f"Persistable{track_type}EmptyTracksContainer" +
+                "_{hash}",
                 allow_duplicate_instances_with_distinct_names=True,
                 outputs={
                     'Output': persistable_location(config['location'])
diff --git a/Hlt/RecoConf/python/RecoConf/muon_reconstruction.py b/Hlt/RecoConf/python/RecoConf/muon_reconstruction.py
index e711133f406bdd25122598957f11ca1d82cd9637..30b76440826ce730ef302ba36a576c820544cd05 100644
--- a/Hlt/RecoConf/python/RecoConf/muon_reconstruction.py
+++ b/Hlt/RecoConf/python/RecoConf/muon_reconstruction.py
@@ -46,8 +46,7 @@ def make_all_muon_pids(tracks, track_types=['Long', 'Downstream']):
 
 
 def make_conv_muon_pids(muonPidsConfs,
-                        best_tracks,
-                        light_reco=True,
+                        best_track_rels,
                         track_types=['Long', 'Downstream']):
     muon_pids_v1 = dict()
     muon_tracks = dict()
@@ -56,19 +55,14 @@ def make_conv_muon_pids(muonPidsConfs,
             # Add muon hits of MuonPID to "muontracks"
             muon_tracks[track_type] = MuonPIDV2ToMuonTracks(
                 name="MuonPIDV2ToMuonTracks_" + track_type + "_{hash}",
-                InputMuonPIDs=muonPidsConfs[track_type],
-                InputTracks=best_tracks[track_type]
-                if light_reco else best_tracks['v1'],
-                RestrictToType=track_type).OutputMuonTracks
+                InputMuonPIDs=muonPidsConfs[track_type]).OutputMuonTracks
 
             # Convert to Keyed Container for ProtoParticle
             muon_pids_v1[track_type] = fromV2MuonPIDV1MuonPID(
                 name="fromV2MuonPIDV1MuonPID" + track_type + "_{hash}",
                 InputMuonPIDs=muonPidsConfs[track_type],
                 InputMuonTracks=muon_tracks[track_type],
-                InputTracks=best_tracks[track_type]
-                if light_reco else best_tracks['v1'],
-                RestrictToType=track_type).OutputMuonPIDs
+                InputTrackRelations=best_track_rels[track_type]).OutputMuonPIDs
         else:
             muon_tracks[track_type] = TracksEmptyProducer(
                 name="MuonTracksEmptyProducer_" + track_type + "_{hash}",
diff --git a/Hlt/RecoConf/python/RecoConf/standalone.py b/Hlt/RecoConf/python/RecoConf/standalone.py
index d437d81a6ce44100210dc40467dcfac60675bea1..f8efb70994e082e5c5346cff2ddf437bb3d29d45 100644
--- a/Hlt/RecoConf/python/RecoConf/standalone.py
+++ b/Hlt/RecoConf/python/RecoConf/standalone.py
@@ -185,8 +185,7 @@ def phoenix_data_dump_hlt2():
 
     # Add Muons
     muonRecConfs = make_all_muon_pids(tracks=tracks_v3)
-    muon_conv, muon_tracks = make_conv_muon_pids(
-        muonRecConfs, hlt2_tracks["BestLong"], light_reco=False)
+    muon_conv, muon_tracks = make_conv_muon_pids(muonRecConfs, trackrels)
     muon_pids = make_merged_muon_pids(muon_conv)
 
     # Adding hits needed for the JSIN dump
@@ -449,8 +448,7 @@ def standalone_hlt2_reco(do_mc_checking=False, do_data_monitoring=False):
 
     # Add Muons
     muonRecConfs = make_all_muon_pids(tracks=tracks_v3)
-    muon_conv, muon_tracks = make_conv_muon_pids(
-        muonRecConfs, best_tracks, light_reco=False)
+    muon_conv, muon_tracks = make_conv_muon_pids(muonRecConfs, trackrels)
     muon_pids = make_merged_muon_pids(muon_conv)
     data += [muon_pids]
 
@@ -595,10 +593,7 @@ def standalone_hlt2_light_reco(fast_reco=False,
 
     muonRecConfs = make_all_muon_pids(
         tracks=tracks_v3, track_types=list(tracks4rich.keys()))
-    muon_conv, muon_tracks = make_conv_muon_pids(
-        muonRecConfs, {k: v['v1']
-                       for k, v in tracks4rich.items()},
-        light_reco=True)
+    muon_conv, muon_tracks = make_conv_muon_pids(muonRecConfs, trackrels)
     muon_pids = make_merged_muon_pids(muon_conv)
     data += [muon_pids]
 
@@ -788,11 +783,7 @@ def standalone_hlt2_light_reco_without_UT(fast_reco=False,
         tracktypes_formuon = list(tracks4rich.keys())
         muonRecConfs = make_all_muon_pids(
             tracks=tracks_v3, track_types=tracktypes_formuon)
-        muon_conv, muon_tracks = make_conv_muon_pids(
-            muonRecConfs, {k: v['v1']
-                           for k, v in tracks4rich.items()},
-            light_reco=True,
-            track_types=tracktypes_formuon)
+        muon_conv, muon_tracks = make_conv_muon_pids(muonRecConfs, trackrels)
         muon_pids = make_merged_muon_pids(muon_conv)
         data += [muon_pids]
 
@@ -966,10 +957,7 @@ def standalone_hlt2_light_reco_ion(fast_reco=False,
 
     muonRecConfs = make_all_muon_pids(
         tracks=tracks_v3, track_types=list(tracks4rich.keys()))
-    muon_pids = make_conv_muon_pids(
-        muonRecConfs, {k: v['v1']
-                       for k, v in tracks4rich.items()},
-        light_reco=True)
+    muon_pids = make_conv_muon_pids(muonRecConfs, trackrels)
     data += [muon_pids]
 
     # proto particles
@@ -1108,11 +1096,7 @@ def standalone_hlt2_light_reco_ion_without_UT(fast_reco=False,
     tracktypes_formuon = list(tracks4rich.keys())
     muonRecConfs = make_all_muon_pids(
         tracks=tracks_v3, track_types=tracktypes_formuon)
-    muon_conv, muon_tracks = make_conv_muon_pids(
-        muonRecConfs,
-        tracks4rich,
-        light_reco=True,
-        track_types=tracktypes_formuon)
+    muon_conv, muon_tracks = make_conv_muon_pids(muonRecConfs, trackrels)
     muon_pids = make_merged_muon_pids(muon_conv)
     data += [muon_pids]