This where i'd minimize the terminal IF I GOT A MINIMIZED FLAG

src/cascadia/TerminalApp/AppActionHandlers.cpp

@@ -596,7 +596,7 @@ namespace winrt::TerminalApp::implementation
     {
         if (const auto& realArgs = args.ActionArgs().try_as<SetMaximizedArgs>())
         {
-            RequestSetMaximized(realArgs.IsMaximized());
+            _RequestSetMaximized(realArgs.IsMaximized());
             args.Handled(true);
         }
     }

src/cascadia/TerminalApp/TerminalPage.cpp

@@ -1,4 +1,4 @@
-
+ShowWindowChanged
 // Copyright (c) Microsoft Corporation.
 // Licensed under the MIT license.
 
@@ -24,7 +24,7 @@
 #include "TabRowControl.h"
 #include "Utils.h"
 
-using namespace winrt;
+    using namespace winrt;
 using namespace winrt::Microsoft::Terminal::Control;
 using namespace winrt::Microsoft::Terminal::Settings::Model;
 using namespace winrt::Microsoft::Terminal::TerminalConnection;
@@ -3568,7 +3568,7 @@ namespace winrt::TerminalApp::implementation
 
     // Method Description:
     // - Asks the window to change its maximized state.
-    void TerminalPage::RequestSetMaximized(bool newMaximized)
+    void TerminalPage::_RequestSetMaximized(bool newMaximized)
     {
         if (_isMaximized == newMaximized)
         {
@@ -3578,6 +3578,20 @@ namespace winrt::TerminalApp::implementation
         _ChangeMaximizeRequestedHandlers(*this, nullptr);
     }
 
+    // Set the window to be minimized. This will bubble it up to the window
+    // layer, and propogate down to the term controls. This should only be used
+    // for an INITIAL defterm connection. We don't really want a `start /min
+    // cmd` to glom to an existing wt and minimize it.
+    void TerminalPage::_RequestSetMinimized()
+    {
+        // Two parts here:
+        // * We need to tell the window layer to minimize the window
+        // * We need to inform the control that we want it to act like it's minimized
+        Microsoft::Terminal::Control::ShowWindowArgs args(false /* show */);
+        _ShowWindowChangedHandlers(*this, args);
+        WindowVisibilityChanged(false);
+    }
+
     HRESULT TerminalPage::_OnNewConnection(const ConptyConnection& connection)
     {
         _newConnectionRevoker.revoke();
@@ -3634,9 +3648,16 @@ namespace winrt::TerminalApp::implementation
             // Make sure that there were no other tabs already existing (in
             // the case that we are in glomming mode), because we don't want
             // to be maximizing other existing sessions that did not ask for it.
-            if (_tabs.Size() == 1 && connection.ShowWindow() == SW_SHOWMAXIMIZED)
+            if (_tabs.Size())
             {
-                RequestSetMaximized(true);
+                if (connection.ShowWindow() == SW_SHOWMAXIMIZED)
+                {
+                    _RequestSetMaximized(true);
+                }
+                else if (connection.ShowWindow() == SW_SHOWMINIMIZED)
+                {
+                    _RequestSetMinimized();
+                }
             }
             return S_OK;
         }

src/cascadia/TerminalApp/TerminalPage.h

@@ -130,7 +130,6 @@ namespace winrt::TerminalApp::implementation
         void SetFullscreen(bool);
         void SetFocusMode(const bool inFocusMode);
         void Maximized(bool newMaximized);
-        void RequestSetMaximized(bool newMaximized);
 
         void SetStartupActions(std::vector<Microsoft::Terminal::Settings::Model::ActionAndArgs>& actions);
 
@@ -524,6 +523,9 @@ namespace winrt::TerminalApp::implementation
         void _SelectionMenuOpened(const IInspectable& sender, const IInspectable& args);
         void _PopulateContextMenu(const IInspectable& sender, const bool withSelection);
 
+        void _RequestSetMaximized(bool newMaximized);
+        void _RequestSetMinimized();
+
 #pragma region ActionHandlers
         // These are all defined in AppActionHandlers.cpp
 #define ON_ALL_ACTIONS(action) DECLARE_ACTION_HANDLER(action);

src/cascadia/TerminalControl/EventArgs.h

@@ -180,3 +180,8 @@ namespace winrt::Microsoft::Terminal::Control::implementation
         WINRT_PROPERTY(bool, ClearMarkers, false);
     };
 }
+
+namespace winrt::Microsoft::Terminal::Control::factory_implementation
+{
+    BASIC_FACTORY(ShowWindowArgs);
+}

src/cascadia/TerminalControl/EventArgs.idl

@@ -81,6 +81,7 @@ namespace Microsoft.Terminal.Control
 
     runtimeclass ShowWindowArgs
     {
+        ShowWindowArgs(Boolean showOrHide);
         Boolean ShowOrHide { get; };
     }