diff --git a/src/gallium/drivers/zink/zink_draw.c b/src/gallium/drivers/zink/zink_draw.c
index 85ae99df517..4cd9502f8a5 100644
--- a/src/gallium/drivers/zink/zink_draw.c
+++ b/src/gallium/drivers/zink/zink_draw.c
@@ -417,8 +417,11 @@ zink_draw_vbo(struct pipe_context *pctx,
    if (ctx->gfx_pipeline_state.vertices_per_patch != dinfo->vertices_per_patch)
       ctx->gfx_pipeline_state.dirty = true;
    bool drawid_broken = ctx->drawid_broken;
-   ctx->drawid_broken = BITSET_TEST(ctx->gfx_stages[PIPE_SHADER_VERTEX]->nir->info.system_values_read, SYSTEM_VALUE_DRAW_ID) &&
-                        (!dindirect || !dindirect->buffer);
+   ctx->drawid_broken = false;
+   if (!dindirect || !dindirect->buffer)
+      ctx->drawid_broken = BITSET_TEST(ctx->gfx_stages[PIPE_SHADER_VERTEX]->nir->info.system_values_read, SYSTEM_VALUE_DRAW_ID) &&
+                           (drawid_offset != 0 ||
+                           ((!ctx->tc || !screen->info.have_EXT_multi_draw) && num_draws > 1));
    if (drawid_broken != ctx->drawid_broken)
       ctx->dirty_shader_stages |= BITFIELD_BIT(PIPE_SHADER_VERTEX);
    ctx->gfx_pipeline_state.vertices_per_patch = dinfo->vertices_per_patch;