diff --git a/draw.h b/draw.h
index 699252a..76e323a 100644
--- a/draw.h
+++ b/draw.h
@@ -178,31 +178,40 @@ static INLINE void draw_quadstrip_colored(const ps1bsp_vertex_t *vertices, const
     }
 }
 
-static INLINE void draw_triangle_textured(STVECTOR *verts, u_short tpage, u_long *ot)
+static INLINE void draw_triangle_textured(const ps1bsp_vertex_t *vertices, const ps1bsp_polyvertex_t *polyVerts, u_short tpage, u_long *ot)
 {
-    // Draw a single textured triangle
-    const STVECTOR *v0 = &verts[0];
-    const STVECTOR *v1 = &verts[1];
-    const STVECTOR *v2 = &verts[2];
+    const ps1bsp_polyvertex_t *v0, *v1, *v2;
 
-    // Naively draw the triangle with GTE, nothing special or optimized about this
-    gte_ldv3(v0, v1, v2);
+    v0 = &polyVerts[0];
+    v1 = &polyVerts[1];
+    v2 = &polyVerts[2];
+
+    // Transform the three vertices
+    gte_ldv3(&vertices[v0->index], &vertices[v1->index], &vertices[v2->index]);
     gte_rtpt();     // Rotation, translation, perspective projection
 
     // Draw a gouraud shaded textured triangle
     POLY_GT3 *poly = (POLY_GT3*)mem_prim(sizeof(POLY_GT3));
-    setPolyGT3(poly);
-    gte_stsxy3_gt3(poly);
 
-    // Texture UVs
-    setUV3(poly, v0->u, v0->v, v1->u, v1->v, v2->u, v2->v);
+    // Fill out the quad's data fields in struct order, to optimize data access
+    // First vertex and texture CLUT
+    setColorFast(&poly->r0, &v0->r);
+    setUVFast(&poly->u0, &v0->u);
+    gte_stsxy0(&poly->x0);
     poly->clut = quake_clut;
+
+    // Second vertex and texture page
+    setColorFast(&poly->r1, &v1->r);
+    gte_stsxy1(&poly->x1);
+    setUVFast(&poly->u1, &v1->u);
     poly->tpage = tpage;
 
-    poly->r0 = poly->g0 = poly->b0 = (uint8_t)v0->pad;
-    poly->r1 = poly->g1 = poly->b1 = (uint8_t)v1->pad;
-    poly->r2 = poly->g2 = poly->b2 = (uint8_t)v2->pad;
+    // Third vertex
+    setColorFast(&poly->r2, &v2->r);
+    gte_stsxy2(&poly->x2);
+    setUVFast(&poly->u2, &v2->u);
 
+    setPolyGT3(poly);
     addPrim(ot, poly);
     ++polyCount;
 }
diff --git a/world.c b/world.c
index e3a4fc4..29b6e3b 100644
--- a/world.c
+++ b/world.c
@@ -147,7 +147,15 @@ static void world_drawface_textured(const world_t *world, const ps1bsp_face_t *f
         for (u_char polyIdx = 0; polyIdx < face->numPolygons; ++polyIdx, ++poly)
         {
             const ps1bsp_polyvertex_t *polyVertices = &world->polyVertices[poly->firstPolyVertex];
-            draw_quadstrip_textured(world->vertices, polyVertices, poly->numPolyVertices, texture->tpage, ot);
+            switch (poly->numPolyVertices)
+            {
+            case 3:
+                draw_triangle_textured(world->vertices, polyVertices, texture->tpage, ot);
+                break;
+            default:
+                draw_quadstrip_textured(world->vertices, polyVertices, poly->numPolyVertices, texture->tpage, ot);
+                break;
+            }
         }
     }
 }