diff --git a/applets/taskmanager/package/contents/code/layout.js b/applets/taskmanager/package/contents/code/layout.js
--- a/applets/taskmanager/package/contents/code/layout.js
+++ b/applets/taskmanager/package/contents/code/layout.js
@@ -17,6 +17,8 @@
  *   51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA .        *
  ***************************************************************************/
 
+var iconSizes = ["small", "smallMedium", "medium", "large", "huge", "enormous"];
+
 function horizontalMargins() {
     return taskFrame.margins.left + taskFrame.margins.right;
 }
@@ -132,7 +134,33 @@
 }
 
 function preferredMaxHeight() {
-    return verticalMargins() + Math.min(units.iconSizes.small * 3, theme.mSize(theme.defaultFont).height * 3);
+    if (tasks.vertical) {
+        return verticalMargins()
+                + Math.min(
+                    // Do not allow the preferred icon size to exceed the width of the vertical task manager.
+                    tasks.width,
+                    Math.max(
+                        // This assumes that we show some text and that we need some minimal vertical space for it.
+                        // In reality, we do not always show the text. We show the text only if there
+                        // is enough horizontal space for some hard coded amount of 'm' characters
+                        // - see minimumMColumns() below.
+                        // Hence in case the user prefers icons smaller than the height of his font,
+                        // the font height will win even if the text will stay invisible.
+                        // We leave it for the future developers to improve this expresssion if the
+                        // named corner case turns out to be important.
+                        units.iconSizes[iconSizes[plasmoid.configuration.iconSize]],
+                        theme.mSize(theme.defaultFont).height
+                    )
+                );
+    } else {
+        return verticalMargins() + Math.min(units.iconSizes.small * 3, theme.mSize(theme.defaultFont).height * 3);
+    }
+}
+
+// Returns the number of 'm' characters whose joint width must be available in the task button label
+// so that the button text is rendered at all.
+function minimumMColumns() {
+    return tasks.vertical ? 4 : 5;
 }
 
 function taskWidth() {
diff --git a/applets/taskmanager/package/contents/config/main.xml b/applets/taskmanager/package/contents/config/main.xml
--- a/applets/taskmanager/package/contents/config/main.xml
+++ b/applets/taskmanager/package/contents/config/main.xml
@@ -101,6 +101,18 @@
       <label>The maximum number of text lines to show in a task button. 0 means no limit.</label>
       <default>0</default>
     </entry>
+    <entry name="iconSize" type="Enum">
+      <label>The preferred size of task button icons in a vertical task manager.</label>
+      <choices>
+            <choice name="small"/>
+            <choice name="smallMedium"/>
+            <choice name="medium"/>
+            <choice name="large"/>
+            <choice name="huge"/>
+            <choice name="enormous"/>
+      </choices>
+      <default>3</default>
+    </entry>
   </group>
 
 </kcfg>
diff --git a/applets/taskmanager/package/contents/ui/ConfigGeneral.qml b/applets/taskmanager/package/contents/ui/ConfigGeneral.qml
--- a/applets/taskmanager/package/contents/ui/ConfigGeneral.qml
+++ b/applets/taskmanager/package/contents/ui/ConfigGeneral.qml
@@ -32,6 +32,7 @@
     readonly property bool plasmaPaAvailable: Qt.createComponent("PulseAudio.qml").status === Component.Ready
 
     property alias cfg_forceStripes: forceStripes.checked
+    property alias cfg_iconSize: iconSize.value
     property alias cfg_showToolTips: showToolTips.checked
     property alias cfg_wheelEnabled: wheelEnabled.checked
     property alias cfg_highlightWindows: highlightWindows.checked
@@ -58,7 +59,7 @@
             flat: true
 
             GridLayout {
-                columns: 2
+                columns: 4
                 Layout.fillWidth: true
 
                 Label {
@@ -68,15 +69,45 @@
                 SpinBox {
                     id: maxStripes
                     minimumValue: 1
+                    Layout.columnSpan: 3
                 }
 
                 CheckBox {
                     id: forceStripes
                     Layout.column: 1
                     Layout.row: 1
                     text: vertical ? i18n("Always arrange tasks in rows of as many columns") : i18n("Always arrange tasks in columns of as many rows")
                     enabled: maxStripes.value > 1
+                    Layout.columnSpan: 3
                 }
+
+                Label {
+                    visible: vertical
+                    text: i18n("Icon size:")
+                }
+
+                Label {
+                    visible: vertical
+                    text: i18n("Small")
+                }
+
+                Slider {
+                    Layout.fillWidth: true
+                    visible: vertical
+                    id: iconSize
+
+                    minimumValue: 0
+                    maximumValue: 5
+                    stepSize: 1
+
+                    tickmarksEnabled: true
+                }
+
+                Label {
+                    visible: vertical
+                    text: i18n("Large")
+                }
+
             }
         }
 
diff --git a/applets/taskmanager/package/contents/ui/Task.qml b/applets/taskmanager/package/contents/ui/Task.qml
--- a/applets/taskmanager/package/contents/ui/Task.qml
+++ b/applets/taskmanager/package/contents/ui/Task.qml
@@ -474,7 +474,7 @@
         id: label
 
         visible: (inPopup || !iconsOnly && model.IsLauncher !== true
-            && (parent.width - iconBox.height - units.smallSpacing) >= (theme.mSize(theme.defaultFont).width * 5))
+            && (parent.width - iconBox.height - units.smallSpacing) >= (theme.mSize(theme.defaultFont).width * LayoutManager.minimumMColumns()))
 
         anchors {
             fill: parent