diff --git a/data/tr1/ship/shaders/sprites.glsl b/data/tr1/ship/shaders/sprites.glsl
index 2f5334e2b..997c24f2a 100644
--- a/data/tr1/ship/shaders/sprites.glsl
+++ b/data/tr1/ship/shaders/sprites.glsl
@@ -1,21 +1,14 @@
-#define NEW_ZBUFFER 0
 #define NEUTRAL_SHADE 0x1000
 
 #ifdef VERTEX
 
 uniform samplerBuffer uUVW; // texture u, v, layer
-uniform vec2 uViewportCenter;
 uniform vec2 uViewportSize;
 uniform mat4 uMatProjection;
-uniform mat4 uMatProjectionOG;
 uniform mat4 uMatModelView;
 uniform float uWibbleOffset;
 uniform vec2 uFog; // x = start, y = end
 
-uniform float uPhdPersp;
-uniform float uPhdResZ;
-uniform float uPhdResZBuf;
-
 layout(location = 0) in vec3 inPosition;
 layout(location = 1) in vec2 inDisplacement;
 layout(location = 2) in int inTextureIdx;
@@ -25,7 +18,6 @@ out vec3 gUV; // x = u, y = v, z = layer
 out float gShade;
 
 void main(void) {
-    #if NEW_ZBUFFER
     vec4 centerEyeSpace = uMatModelView * vec4(inPosition, 1.0);
     centerEyeSpace.xy += inDisplacement;
     gl_Position = uMatProjection * centerEyeSpace;
@@ -34,26 +26,6 @@ void main(void) {
         gl_Position.xyz =
             waterWibble(gl_Position, uViewportSize, uWibbleOffset);
     }
-    #else
-    vec3 localPos = inPosition;
-    vec3 worldPos = (uMatModelView * vec4(localPos, 1)).xyz;
-
-    if ((uMatProjection * vec4(worldPos, 1)).z <= 0) {
-        // Terrible hack:
-        // Push the vertex out of view (e.g. offscreen or behind clip).
-        // Works for entire sprites, because worldPos is the position of the
-        // sprite origin, the same for all vertices.
-        gl_Position = vec4(2.0, 2.0, 1.0, 1.0);
-        return;
-    }
-
-    vec3 screenCenterPos = vec3(
-        uViewportCenter + worldPos.xy * uPhdPersp / worldPos.z,
-        uPhdResZBuf - uPhdResZ / worldPos.z);
-    vec3 screenCornerPos = screenCenterPos;
-    screenCornerPos.xy += inDisplacement * uPhdPersp / worldPos.z;
-    gl_Position = (uMatProjectionOG * vec4(screenCornerPos, 1));
-    #endif
 
     gUV = texelFetch(uUVW, int(inTextureIdx)).xyz;
     gShade = inShade;
diff --git a/src/tr1/game/output.c b/src/tr1/game/output.c
index f9c27f567..7c6630ff2 100644
--- a/src/tr1/game/output.c
+++ b/src/tr1/game/output.c
@@ -1409,14 +1409,8 @@ void Output_GetProjectionMatrix(GLfloat output[][4])
 
     output[2][0] = 0.0f;
     output[2][1] = 0.0f;
-    // TODO(dash): these do not match the original game Z buffer mapping.
-    // I couldn't figure out how to replicate the original MAP_DEPTH transform.
-    // To combat this, the vertex shaders for now fence the simpler matrices
-    // behind a `NEW_ZBUFFER` define, and fall back to doing the perspective
-    // transform completely manually. This will be removable once we no longer
-    // rely on PHD_VBUF / GFX_3D_Rendere for world rendering.
-    output[2][2] = (far + near) / (far - near);
-    output[2][3] = -(2.0f * far * near) / (far - near);
+    output[2][2] = g_FltResZBuf;
+    output[2][3] = -g_FltResZ / (float)(1 << W2V_SHIFT);
 
     output[3][0] = 0.0f;
     output[3][1] = 0.0f;
diff --git a/src/tr1/game/output/sprite_program.c b/src/tr1/game/output/sprite_program.c
index eab887c5a..b09363eae 100644
--- a/src/tr1/game/output/sprite_program.c
+++ b/src/tr1/game/output/sprite_program.c
@@ -13,13 +13,8 @@ typedef enum {
     M_UNIFORM_SMOOTHING_ENABLED,
     M_UNIFORM_BRIGHTNESS_MULTIPLIER,
     M_UNIFORM_GLOBAL_TINT,
-    M_UNIFORM_VIEWPORT_CENTER,
     M_UNIFORM_VIEWPORT_SIZE,
     M_UNIFORM_PROJECTION_MATRIX,
-    M_UNIFORM_PROJECTION_MATRIX_OG,
-    M_UNIFORM_PHD_PERSP,
-    M_UNIFORM_PHD_RES_Z,
-    M_UNIFORM_PHD_RES_Z_BUF,
     M_UNIFORM_MODEL_MATRIX,
     M_UNIFORM_WIBBLE_OFFSET,
     M_UNIFORM_NUMBER_OF,
@@ -46,13 +41,8 @@ void Output_SpriteProgram_Init(void)
         [M_UNIFORM_SMOOTHING_ENABLED] = "uSmoothingEnabled",
         [M_UNIFORM_BRIGHTNESS_MULTIPLIER] = "uBrightnessMultiplier",
         [M_UNIFORM_GLOBAL_TINT] = "uGlobalTint",
-        [M_UNIFORM_VIEWPORT_CENTER] = "uViewportCenter",
         [M_UNIFORM_VIEWPORT_SIZE] = "uViewportSize",
         [M_UNIFORM_PROJECTION_MATRIX] = "uMatProjection",
-        [M_UNIFORM_PROJECTION_MATRIX_OG] = "uMatProjectionOG",
-        [M_UNIFORM_PHD_PERSP] = "uPhdPersp",
-        [M_UNIFORM_PHD_RES_Z] = "uPhdResZ",
-        [M_UNIFORM_PHD_RES_Z_BUF] = "uPhdResZBuf",
         [M_UNIFORM_MODEL_MATRIX] = "uMatModelView",
         [M_UNIFORM_WIBBLE_OFFSET] = "uWibbleOffset",
     };
@@ -86,9 +76,6 @@ void Output_SpriteProgram_UploadCommonUniforms(void)
     GFX_TRACK_UNIFORM(
         glUniform1f, m_Uniforms[M_UNIFORM_BRIGHTNESS_MULTIPLIER],
         g_Config.visuals.brightness);
-    GFX_TRACK_UNIFORM(
-        glUniform2f, m_Uniforms[M_UNIFORM_VIEWPORT_CENTER],
-        Viewport_GetCenterX(), Viewport_GetCenterY());
     GFX_TRACK_UNIFORM(
         glUniform2f, m_Uniforms[M_UNIFORM_VIEWPORT_SIZE],
         GFX_Context_GetDisplayWidth(), GFX_Context_GetDisplayHeight());
@@ -135,28 +122,6 @@ void Output_SpriteProgram_UploadProjectionMatrix(void)
     GFX_TRACK_UNIFORM(
         glUniformMatrix4fv, m_Uniforms[M_UNIFORM_PROJECTION_MATRIX], 1, GL_TRUE,
         &projection[0][0]);
-
-    const float left = 0.0f;
-    const float top = 0.0f;
-    const float right = GFX_Context_GetDisplayWidth();
-    const float bottom = GFX_Context_GetDisplayHeight();
-    GLfloat projection_og[4][4] = {
-        { 2.0f / (right - left), 0.0f, 0.0f, 0.0f },
-        { 0.0f, 2.0f / (top - bottom), 0.0f, 0.0f },
-        { 0.0f, 0.0f, +1.0f, 0.0f },
-        { -(right + left) / (right - left), -(top + bottom) / (top - bottom),
-          0.0f, 1.0f },
-    };
-    GFX_TRACK_UNIFORM(
-        glUniformMatrix4fv, m_Uniforms[M_UNIFORM_PROJECTION_MATRIX_OG], 1,
-        GL_FALSE, &projection_og[0][0]);
-
-    GFX_TRACK_UNIFORM(glUniform1f, m_Uniforms[M_UNIFORM_PHD_PERSP], g_PhdPersp);
-    GFX_TRACK_UNIFORM(
-        glUniform1f, m_Uniforms[M_UNIFORM_PHD_RES_Z],
-        g_FltResZ / (float)(1 << W2V_SHIFT));
-    GFX_TRACK_UNIFORM(
-        glUniform1f, m_Uniforms[M_UNIFORM_PHD_RES_Z_BUF], g_FltResZBuf);
 }
 
 void Output_SpriteProgram_UploadTint(const RGB_F tint)