diff --git a/Core/Core.h b/Core/Core.h
index 0b20d2ac6a..d867e8b439 100644
--- a/Core/Core.h
+++ b/Core/Core.h
@@ -26,7 +26,7 @@
 
 class GraphicsContext;
 
-// For platforms that don't call Core_Run
+// For platforms that don't call Run
 void Core_SetGraphicsContext(GraphicsContext *ctx);
 
 // Returns false when an UI exit state is detected.
diff --git a/GPU/Debugger/Playback.cpp b/GPU/Debugger/Playback.cpp
index 11f8a81684..8073440c0b 100644
--- a/GPU/Debugger/Playback.cpp
+++ b/GPU/Debugger/Playback.cpp
@@ -100,7 +100,7 @@ protected:
 		u32 buf_pointer_ = 0;
 		int last_used_ = 0;
 
-		bool Matches(u32 bufpos) {
+		bool Matches(u32 bufpos) const {
 			// We check psp_pointer_ because bufpos = 0 is valid, and the initial value.
 			return buf_pointer_ == bufpos && psp_pointer_ != 0;
 		}
@@ -130,12 +130,12 @@ protected:
 		u32 buf_pointer_ = 0;
 		u32 size_ = 0;
 
-		bool Matches(u32 bufpos, u32 sz) {
+		bool Matches(u32 bufpos, u32 sz) const {
 			// We check psp_pointer_ because bufpos = 0 is valid, and the initial value.
 			return buf_pointer_ == bufpos && psp_pointer_ != 0 && size_ >= sz;
 		}
 
-		u32 Ptr() {
+		u32 Ptr() const {
 			return psp_pointer_;
 		}
 
diff --git a/Windows/EmuThread.cpp b/Windows/EmuThread.cpp
index 4f0c1924c1..2e20d21b5b 100644
--- a/Windows/EmuThread.cpp
+++ b/Windows/EmuThread.cpp
@@ -75,7 +75,7 @@ bool MainThread_Ready() {
 	return g_inLoop;
 }
 
-static bool Core_Run(GraphicsContext *ctx) {
+static bool Run(GraphicsContext *ctx) {
 	System_Notify(SystemNotification::DISASSEMBLY);
 	while (true) {
 		if (GetUIState() != UISTATE_INGAME) {
@@ -127,11 +127,11 @@ static void EmuThreadFunc(GraphicsContext *graphicsContext) {
 	NativeInitGraphics(graphicsContext);
 
 	while (emuThreadState != (int)EmuThreadState::QUIT_REQUESTED) {
-		// We're here again, so the game quit.  Restart Core_Run() which controls the UI.
+		// We're here again, so the game quit.  Restart Run() which controls the UI.
 		// This way they can load a new game.
 		if (!Core_IsActive())
 			UpdateUIState(UISTATE_MENU);
-		if (!Core_Run(g_graphicsContext)) {
+		if (!Run(g_graphicsContext)) {
 			emuThreadState = (int)EmuThreadState::QUIT_REQUESTED;
 		}
 	}
@@ -338,11 +338,11 @@ void MainThreadFunc() {
 		}
 	} else {
 		while (GetUIState() != UISTATE_EXIT) {  //  && GetUIState() != UISTATE_EXCEPTION
-			// We're here again, so the game quit.  Restart Core_Run() which controls the UI.
+			// We're here again, so the game quit.  Restart Run() which controls the UI.
 			// This way they can load a new game.
 			if (!Core_IsActive())
 				UpdateUIState(UISTATE_MENU);
-			Core_Run(g_graphicsContext);
+			Run(g_graphicsContext);
 			if (coreState == CORE_BOOT_ERROR) {
 				break;
 			}
@@ -351,7 +351,7 @@ void MainThreadFunc() {
 	Core_Stop();
 	if (!useEmuThread) {
 		// Process the shutdown.  Without this, non-GL delays 800ms on shutdown.
-		Core_Run(g_graphicsContext);
+		Run(g_graphicsContext);
 	}
 	Core_WaitInactive();