diff --git a/OpenRA.Mods.Common/Activities/LegacyEnter.cs b/OpenRA.Mods.Common/Activities/LegacyEnter.cs
index 9b5837496d..0e5befd085 100644
--- a/OpenRA.Mods.Common/Activities/LegacyEnter.cs
+++ b/OpenRA.Mods.Common/Activities/LegacyEnter.cs
@@ -205,7 +205,7 @@ namespace OpenRA.Mods.Common.Activities
 					isEnteringOrInside = true;
 					savedPos = self.CenterPosition; // Save position of self, before entering, for returning on exit
 
-					inner = move.MoveIntoTarget(self, target); // Enter
+					inner = move.VisualMove(self, self.CenterPosition,  target.Positions.PositionClosestTo(self.CenterPosition));
 
 					if (inner != null)
 					{
@@ -228,7 +228,7 @@ namespace OpenRA.Mods.Common.Activities
 						Unreserve(self, false);
 						if (Reserve(self) == ReserveStatus.Ready)
 						{
-							inner = move.MoveIntoTarget(self, target); // Enter
+							inner = move.VisualMove(self, self.CenterPosition, target.Positions.PositionClosestTo(self.CenterPosition));
 							if (inner != null)
 								return EnterState.ApproachingOrEntering;
 
diff --git a/OpenRA.Mods.Common/Activities/Move/VisualMoveIntoTarget.cs b/OpenRA.Mods.Common/Activities/Move/VisualMoveIntoTarget.cs
new file mode 100644
index 0000000000..48b93d7259
--- /dev/null
+++ b/OpenRA.Mods.Common/Activities/Move/VisualMoveIntoTarget.cs
@@ -0,0 +1,97 @@
+#region Copyright & License Information
+/*
+ * Copyright 2007-2019 The OpenRA Developers (see AUTHORS)
+ * This file is part of OpenRA, which is free software. It is made
+ * available to you under the terms of the GNU General Public License
+ * as published by the Free Software Foundation, either version 3 of
+ * the License, or (at your option) any later version. For more
+ * information, see COPYING.
+ */
+#endregion
+
+using System.Collections.Generic;
+using OpenRA.Activities;
+using OpenRA.Mods.Common.Traits;
+using OpenRA.Traits;
+
+namespace OpenRA.Mods.Common.Activities
+{
+	public class VisualMoveIntoTarget : Activity
+	{
+		readonly Mobile mobile;
+		readonly Target target;
+		readonly WDist targetMovementThreshold;
+		WPos targetStartPos;
+
+		public VisualMoveIntoTarget(Actor self, Target target, WDist targetMovementThreshold)
+		{
+			mobile = self.Trait<Mobile>();
+			this.target = target;
+			this.targetMovementThreshold = targetMovementThreshold;
+		}
+
+		protected override void OnFirstRun(Actor self)
+		{
+			targetStartPos = target.Positions.PositionClosestTo(self.CenterPosition);
+			mobile.IsMoving = true;
+		}
+
+		public override Activity Tick(Actor self)
+		{
+			if (ChildActivity != null)
+			{
+				ChildActivity = ActivityUtils.RunActivity(self, ChildActivity);
+				if (ChildActivity != null)
+					return this;
+			}
+
+			if (IsCanceled || target.Type == TargetType.Invalid)
+				return NextActivity;
+
+			if (mobile.IsTraitDisabled)
+				return this;
+
+			var currentPos = self.CenterPosition;
+			var targetPos = target.Positions.PositionClosestTo(currentPos);
+
+			// Give up if the target has moved too far
+			if (targetMovementThreshold > WDist.Zero && (targetPos - targetStartPos).LengthSquared > targetMovementThreshold.LengthSquared)
+				return NextActivity;
+
+			// Turn if required
+			var delta = targetPos - currentPos;
+			var facing = delta.HorizontalLengthSquared != 0 ? delta.Yaw.Facing : mobile.Facing;
+			if (facing != mobile.Facing)
+			{
+				var turn = ActivityUtils.RunActivity(self, new Turn(self, facing));
+				if (turn != null)
+					QueueChild(turn);
+
+				return this;
+			}
+
+			// Can complete the move in this step
+			var speed = mobile.MovementSpeedForCell(self, self.Location);
+			if (delta.LengthSquared <= speed * speed)
+			{
+				mobile.SetVisualPosition(self, targetPos);
+				return NextActivity;
+			}
+
+			// Move towards the target
+			mobile.SetVisualPosition(self, currentPos + delta * speed / delta.Length);
+
+			return this;
+		}
+
+		protected override void OnLastRun(Actor self)
+		{
+			mobile.IsMoving = false;
+		}
+
+		public override IEnumerable<Target> GetTargets(Actor self)
+		{
+			yield return target;
+		}
+	}
+}
diff --git a/OpenRA.Mods.Common/OpenRA.Mods.Common.csproj b/OpenRA.Mods.Common/OpenRA.Mods.Common.csproj
index 8c3df4e4cd..d50c0b5587 100644
--- a/OpenRA.Mods.Common/OpenRA.Mods.Common.csproj
+++ b/OpenRA.Mods.Common/OpenRA.Mods.Common.csproj
@@ -103,6 +103,7 @@
     <Compile Include="Activities\Move\Move.cs" />
     <Compile Include="Activities\Move\MoveAdjacentTo.cs" />
     <Compile Include="Activities\Move\MoveWithinRange.cs" />
+    <Compile Include="Activities\Move\VisualMoveIntoTarget.cs" />
     <Compile Include="Activities\Parachute.cs" />
     <Compile Include="Activities\Rearm.cs" />
     <Compile Include="Activities\RemoveSelf.cs" />
diff --git a/OpenRA.Mods.Common/Traits/Mobile.cs b/OpenRA.Mods.Common/Traits/Mobile.cs
index 68ec3b8f28..a94afc7f5f 100644
--- a/OpenRA.Mods.Common/Traits/Mobile.cs
+++ b/OpenRA.Mods.Common/Traits/Mobile.cs
@@ -517,7 +517,9 @@ namespace OpenRA.Mods.Common.Traits
 			if (target.Type == TargetType.Invalid)
 				return null;
 
-			return VisualMove(self, self.CenterPosition, target.Positions.PositionClosestTo(self.CenterPosition));
+			// Activity cancels if the target moves by more than half a cell
+			// to avoid problems with the cell grid
+			return new VisualMoveIntoTarget(self, target, new WDist(512));
 		}
 
 		public Activity VisualMove(Actor self, WPos fromPos, WPos toPos)