diff --git a/src/gallium/auxiliary/gallivm/lp_bld_limits.h b/src/gallium/auxiliary/gallivm/lp_bld_limits.h
index 49064feddef..db503514881 100644
--- a/src/gallium/auxiliary/gallivm/lp_bld_limits.h
+++ b/src/gallium/auxiliary/gallivm/lp_bld_limits.h
@@ -51,8 +51,12 @@
 
 #define LP_MAX_TGSI_PREDS 16
 
+#define LP_MAX_TGSI_CONSTS 4096
+
 #define LP_MAX_TGSI_CONST_BUFFERS 16
 
+#define LP_MAX_TGSI_CONST_BUFFER_SIZE (LP_MAX_TGSI_CONSTS * sizeof(float[4]))
+
 /*
  * For quick access we cache registers in statically
  * allocated arrays. Here we define the maximum size
@@ -100,7 +104,7 @@ gallivm_get_shader_param(enum pipe_shader_cap param)
    case PIPE_SHADER_CAP_MAX_OUTPUTS:
       return 32;
    case PIPE_SHADER_CAP_MAX_CONST_BUFFER_SIZE:
-      return sizeof(float[4]) * 4096;
+      return LP_MAX_TGSI_CONST_BUFFER_SIZE;
    case PIPE_SHADER_CAP_MAX_CONST_BUFFERS:
       return PIPE_MAX_CONSTANT_BUFFERS;
    case PIPE_SHADER_CAP_MAX_TEMPS:
diff --git a/src/gallium/drivers/llvmpipe/lp_setup.c b/src/gallium/drivers/llvmpipe/lp_setup.c
index 56292c68c5f..4c8167a9e7d 100644
--- a/src/gallium/drivers/llvmpipe/lp_setup.c
+++ b/src/gallium/drivers/llvmpipe/lp_setup.c
@@ -1069,10 +1069,13 @@ try_update_scene_state( struct lp_setup_context *setup )
    if (setup->dirty & LP_SETUP_NEW_CONSTANTS) {
       for (i = 0; i < Elements(setup->constants); ++i) {
          struct pipe_resource *buffer = setup->constants[i].current.buffer;
-         const unsigned current_size = setup->constants[i].current.buffer_size;
+         const unsigned current_size = MIN2(setup->constants[i].current.buffer_size,
+                                            LP_MAX_TGSI_CONST_BUFFER_SIZE);
          const ubyte *current_data = NULL;
          int num_constants;
 
+         STATIC_ASSERT(DATA_BLOCK_SIZE >= LP_MAX_TGSI_CONST_BUFFER_SIZE);
+
          if (buffer) {
             /* resource buffer */
             current_data = (ubyte *) llvmpipe_resource_data(buffer);