diff --git a/core/bounds.gms b/core/bounds.gms
index 165215412..6f37fc7d6 100755
--- a/core/bounds.gms
+++ b/core/bounds.gms
@@ -535,8 +535,8 @@ v_shfe.lo(t,regi,entyFe,sector)$pm_shfe_lo(t,regi,entyFe,sector) = pm_shfe_lo(t,
 v_shGasLiq_fe.up(t,regi,sector)$pm_shGasLiq_fe_up(t,regi,sector) = pm_shGasLiq_fe_up(t,regi,sector);
 v_shGasLiq_fe.lo(t,regi,sector)$pm_shGasLiq_fe_lo(t,regi,sector) = pm_shGasLiq_fe_lo(t,regi,sector);
 
-*** RH: Fix H2 in buildings to zero until given year (always zero by default)
-vm_demFeSector.up(t,regi,"seh2","feh2s","build",emiMkt)$(t.val le c_H2InBuildOnlyAfter) = 0;
+*** Set H2 upper bound in buildings for years defined at c_H2InBuildOnlyAfter
+vm_demFeSector.up(t,regi,"seh2","feh2s","build",emiMkt)$(t.val le c_H2InBuildOnlyAfter) = 1e-6;
 
 ***----------------------------------------------------------------------------
 ***  Controlling if active, dampening factor to align edge-t non-energy transportation costs with historical GDP data
diff --git a/modules/29_CES_parameters/calibrate/datainput.gms b/modules/29_CES_parameters/calibrate/datainput.gms
index cbb008ad7..b3683514d 100644
--- a/modules/29_CES_parameters/calibrate/datainput.gms
+++ b/modules/29_CES_parameters/calibrate/datainput.gms
@@ -305,15 +305,18 @@ $ifthen.build_H2_offset "%buildings%" == "simple"
 *);
 
 *** RK: feh2b offset scaled from 1% in 2025 to 50% in 2050 of fegab quantity
-loop ((t,regi),
-	pm_cesdata(t,regi,"feh2b","offset_quantity")
-  = - (0.05 + 0.45 * min(1, max(0, (t.val - 2025) / (2050 - 2025))))
-      * pm_cesdata(t,regi,"fegab","quantity")
-    - pm_cesdata(t,regi,"feh2b","quantity");
-      pm_cesdata(t,regi,"feh2b","quantity")
-  = (0.05 + 0.45 * min(1, max(0, (t.val - 2025) / (2050 - 2025))))
-      * pm_cesdata(t,regi,"fegab","quantity");
-);
+pm_cesdata(t,regi,"feh2b","offset_quantity")$(t.val gt c_H2InBuildOnlyAfter) =
+  - (0.05 + 0.45 * min(1, max(0, (t.val - 2025) / (2050 - 2025))))
+    * pm_cesdata(t,regi,"fegab","quantity")
+  - pm_cesdata(t,regi,"feh2b","quantity");
+pm_cesdata(t,regi,"feh2b","quantity")$(t.val gt c_H2InBuildOnlyAfter) = 
+  (0.05 + 0.45 * min(1, max(0, (t.val - 2025) / (2050 - 2025))))
+    * pm_cesdata(t,regi,"fegab","quantity");
+
+*** for the years that H2 buildings is fixed to zero, set offset to the exact value of the calibrated quantity to ignore it after calibration
+pm_cesdata(t,regi,"feh2b","quantity")$(t.val le c_H2InBuildOnlyAfter) = 1e-6;
+pm_cesdata(t,regi,"feh2b","offset_quantity")$(t.val le c_H2InBuildOnlyAfter) = - pm_cesdata(t,regi,"feh2b","quantity");
+
 $endif.build_H2_offset
 
 *** Add an epsilon to the values which are 0 so that they can fit in the CES
diff --git a/modules/36_buildings/simple/equations.gms b/modules/36_buildings/simple/equations.gms
index bea5febef..c2c640915 100644
--- a/modules/36_buildings/simple/equations.gms
+++ b/modules/36_buildings/simple/equations.gms
@@ -65,7 +65,7 @@ q36_auxCostAddTeInv(t,regi)..
 
 
 *' Hydrogen fe share in buildings gases use (natural gas + hydrogen)
-q36_H2Share(t,regi)..
+q36_H2Share(t,regi)$(t.val ge 2020)..
   v36_H2share(t,regi) 
   * sum(se2fe(entySe,entyFe,te)$(SAMEAS(entyFe,"feh2s")
                                  OR SAMEAS(entyFe,"fegas")),