diff --git a/stepmania/src/RageTexture.cpp b/stepmania/src/RageTexture.cpp
index 0071e34608..5768f48662 100644
--- a/stepmania/src/RageTexture.cpp
+++ b/stepmania/src/RageTexture.cpp
@@ -25,17 +25,25 @@ void RageTextureID::Init()
 	bHotPinkColorKey = false;
 }
 
-bool RageTextureID::equal(const RageTextureID &rhs) const
+bool RageTextureID::operator<(const RageTextureID &rhs) const
 {
-	if(filename != rhs.filename) return false;
-	if(iMaxSize != rhs.iMaxSize) return false;
-	if(iMipMaps != rhs.iMipMaps) return false;
-	if(iAlphaBits != rhs.iAlphaBits) return false;
-	if(iColorDepth != rhs.iColorDepth) return false;
-	if(bDither != rhs.bDither) return false;
-	if(bStretch != rhs.bStretch) return false;
-	if(bHotPinkColorKey != rhs.bHotPinkColorKey) return false;
-	return true;
+	if(filename < rhs.filename) return true;
+	if(filename > rhs.filename) return false;
+	if(iMaxSize < rhs.iMaxSize) return true;
+	if(iMaxSize > rhs.iMaxSize) return false;
+	if(iMipMaps < rhs.iMipMaps) return true;
+	if(iMipMaps > rhs.iMipMaps) return false;
+	if(iAlphaBits < rhs.iAlphaBits) return true;
+	if(iAlphaBits > rhs.iAlphaBits) return false;
+	if(iColorDepth < rhs.iColorDepth) return true;
+	if(iColorDepth > rhs.iColorDepth) return false;
+	if(bDither < rhs.bDither) return true;
+	if(bDither > rhs.bDither) return false;
+	if(bStretch < rhs.bStretch) return true;
+	if(bStretch > rhs.bStretch) return false;
+	if(bHotPinkColorKey < rhs.bHotPinkColorKey) return true;
+	if(bHotPinkColorKey > rhs.bHotPinkColorKey) return false;
+	return false;
 }
 
 
diff --git a/stepmania/src/RageTexture.h b/stepmania/src/RageTexture.h
index 64c4decc3c..a10ece5a65 100644
--- a/stepmania/src/RageTexture.h
+++ b/stepmania/src/RageTexture.h
@@ -31,10 +31,7 @@ struct RageTextureID
 	bool bStretch;
 	bool bHotPinkColorKey; /* #FF00FF */
 
-	/* Define an ordering so this can be used in a set<>.  This defines a partial
-	 * ordering; use equal() to see if they're equal. */
-	bool operator< (const RageTextureID &rhs) const	{ return filename < rhs.filename; }
-	bool equal(const RageTextureID &rhs) const;
+	bool operator< (const RageTextureID &rhs) const;
 
 	void Init();
 
diff --git a/stepmania/src/RageTextureManager.cpp b/stepmania/src/RageTextureManager.cpp
index fd24682160..98f71bdd69 100644
--- a/stepmania/src/RageTextureManager.cpp
+++ b/stepmania/src/RageTextureManager.cpp
@@ -76,15 +76,9 @@ RageTexture* RageTextureManager::LoadTexture( RageTextureID ID )
 	std::map<RageTextureID, RageTexture*>::iterator p = m_mapPathToTexture.find(ID);
 	while(p != m_mapPathToTexture.end())
 	{
-		if(p->first.equal(ID)) {
-			/* Found the texture.  Just increase the refcount and return it. */
-			p->second->m_iRefCount++;
-			return p->second;
-		}
-
-		/* short circuit */
-		if(p->first.filename > ID.filename) break;
-		p++;
+		/* Found the texture.  Just increase the refcount and return it. */
+		p->second->m_iRefCount++;
+		return p->second;
 	}
 
 	// the texture is not already loaded.  Load it.