diff --git a/pkg/controller/plan/migration.go b/pkg/controller/plan/migration.go
index eaee3b200..122ebffb2 100644
--- a/pkg/controller/plan/migration.go
+++ b/pkg/controller/plan/migration.go
@@ -1146,7 +1146,7 @@ func (r *Migration) execute(vm *plan.VMStatus) (err error) {
 				return err
 			}
 
-			if pod != nil && pod.Status.Phase != core.PodSucceeded {
+			if pod != nil && pod.Status.Phase == core.PodRunning {
 				err := r.kubevirt.UpdateVmByConvertedConfig(vm, pod, step)
 				if err != nil {
 					return liberr.Wrap(err)
diff --git a/pkg/controller/plan/scheduler/vsphere/scheduler.go b/pkg/controller/plan/scheduler/vsphere/scheduler.go
index 0b2abef98..6d59be80b 100644
--- a/pkg/controller/plan/scheduler/vsphere/scheduler.go
+++ b/pkg/controller/plan/scheduler/vsphere/scheduler.go
@@ -14,6 +14,21 @@ import (
 	liberr "github.com/konveyor/forklift-controller/pkg/lib/error"
 )
 
+// Phases.
+const (
+	CopyingPaused            = "CopyingPaused"
+	CreateGuestConversionPod = "CreateGuestConversionPod"
+	ConvertGuest             = "ConvertGuest"
+	CreateVM                 = "CreateVM"
+	PostHook                 = "PostHook"
+	Completed                = "Completed"
+)
+
+// Steps.
+const (
+	DiskTransfer = "DiskTransfer"
+)
+
 // Package level mutex to ensure that
 // multiple concurrent reconciles don't
 // attempt to schedule VMs into the same
@@ -107,7 +122,7 @@ func (r *Scheduler) buildInFlight() (err error) {
 			return
 		}
 		if vmStatus.Running() {
-			r.inFlight[vm.Host] += r.cost(vm)
+			r.inFlight[vm.Host] += r.cost(vm, vmStatus)
 		}
 	}
 
@@ -153,7 +168,7 @@ func (r *Scheduler) buildInFlight() (err error) {
 				}
 				return err
 			}
-			r.inFlight[vm.Host] += r.cost(vm)
+			r.inFlight[vm.Host] += r.cost(vm, vmStatus)
 		}
 	}
 
@@ -170,11 +185,10 @@ func (r *Scheduler) buildPending() (err error) {
 		if err != nil {
 			return
 		}
-
 		if !vmStatus.MarkedStarted() && !vmStatus.MarkedCompleted() {
 			pending := &pendingVM{
 				status: vmStatus,
-				cost:   r.cost(vm),
+				cost:   r.cost(vm, vmStatus),
 			}
 			r.pending[vm.Host] = append(r.pending[vm.Host], pending)
 		}
@@ -182,16 +196,47 @@ func (r *Scheduler) buildPending() (err error) {
 	return
 }
 
-func (r *Scheduler) cost(vm *model.VM) int {
-	if coldLocal, _ := r.Plan.VSphereColdLocal(); coldLocal {
-		/// virt-v2v transfers one disk at a time
-		return 1
+func (r *Scheduler) cost(vm *model.VM, vmStatus *plan.VMStatus) int {
+	coldLocal, _ := r.Plan.VSphereColdLocal()
+	if coldLocal {
+		switch vmStatus.Phase {
+		case CreateVM, PostHook, Completed:
+			// In these phases we already have the disk transferred and are left only to create the VM
+			// By setting the cost to 0 other VMs can start migrating
+			return 0
+		default:
+			return 1
+		}
 	} else {
-		// CDI transfers the disks in parallel by different pods
-		return len(vm.Disks)
+		switch vmStatus.Phase {
+		case CreateVM, PostHook, Completed, CopyingPaused, ConvertGuest, CreateGuestConversionPod:
+			// The warm/remote migrations this is done on already transferred disks,
+			// and we can start other VM migrations at these point.
+			// By setting the cost to 0 other VMs can start migrating
+			return 0
+		default:
+			// CDI transfers the disks in parallel by different pods
+			return len(vm.Disks) - r.finishedDisks(vmStatus)
+		}
 	}
 }
 
+// finishedDisks returns a number of the disks that have completed the disk transfer
+// This can reduce the migration time as VMs with one large disks and many small disks won't halt the scheduler
+func (r *Scheduler) finishedDisks(vmStatus *plan.VMStatus) int {
+	var resp = 0
+	for _, step := range vmStatus.Pipeline {
+		if step.Name == "DiskTransfer" {
+			for _, task := range step.Tasks {
+				if task.Phase == "Completed" {
+					resp += 1
+				}
+			}
+		}
+	}
+	return resp
+}
+
 // Return a map of all the VMs that could be scheduled
 // based on the available host capacities.
 func (r *Scheduler) schedulable() (schedulable map[string][]*pendingVM) {
@@ -204,6 +249,11 @@ func (r *Scheduler) schedulable() (schedulable map[string][]*pendingVM) {
 			if vms[i].cost+r.inFlight[host] <= r.MaxInFlight {
 				schedulable[host] = append(schedulable[host], vms[i])
 			}
+			// In case there is VM with more disks than the MaxInFlight MTV will migrate it, if there are no other VMs
+			// being migrated at that time.
+			if vms[i].cost > r.MaxInFlight && r.inFlight[host] == 0 {
+				schedulable[host] = append(schedulable[host], vms[i])
+			}
 		}
 	}
 
diff --git a/virt-v2v/cmd/entrypoint.go b/virt-v2v/cmd/entrypoint.go
index 58a2f1d79..ca9b34a58 100644
--- a/virt-v2v/cmd/entrypoint.go
+++ b/virt-v2v/cmd/entrypoint.go
@@ -134,12 +134,6 @@ func virtV2vBuildCommand() (args []string, err error) {
 		args = append(args, "-i", "ova", os.Getenv("V2V_diskPath"))
 	}
 
-	// When converting VM with name that do not meet DNS1123 RFC requirements,
-	// it should be changed to supported one to ensure the conversion does not fail.
-	if utils.CheckEnvVariablesSet("V2V_NewName") {
-		args = append(args, "-on", os.Getenv("V2V_NewName"))
-	}
-
 	return args, nil
 }
 
@@ -158,6 +152,12 @@ func virtV2vVsphereArgs() (args []string, err error) {
 		)
 	}
 
+	// When converting VM with name that do not meet DNS1123 RFC requirements,
+	// it should be changed to supported one to ensure the conversion does not fail.
+	if utils.CheckEnvVariablesSet("V2V_NewName") {
+		args = append(args, "-on", os.Getenv("V2V_NewName"))
+	}
+
 	args = append(args, "--", os.Getenv("V2V_vmName"))
 	return args, nil
 }