diff --git a/source/MRViewer/MRGLStaticHolder.cpp b/source/MRViewer/MRGLStaticHolder.cpp
index 26f3aac04f66..df82745c95c5 100644
--- a/source/MRViewer/MRGLStaticHolder.cpp
+++ b/source/MRViewer/MRGLStaticHolder.cpp
@@ -182,7 +182,14 @@ void GLStaticHolder::createShader_( ShaderType type )
   out vec3 world_pos;
   out float primitiveIdf0;
   out float primitiveIdf1;
-
+)"
+#ifndef __EMSCRIPTEN__
+            // desktop GL has integer varyings, so the id needs no float round-trip
+            R"(
+  flat out uint primitiveIdFlat;
+)"
+#endif
+            R"(
   void main()
   {
     world_pos = vec3(model*vec4 (position, 1.0));
@@ -190,6 +197,13 @@ void GLStaticHolder::createShader_( ShaderType type )
     uint primId = uint(gl_VertexID) / primBucketSize;
     primitiveIdf1 = float( uint( primId >> 20u ) ) + 0.5;
     primitiveIdf0 = float( primId % uint( 1u << 20u ) ) + 0.5;
+)"
+#ifndef __EMSCRIPTEN__
+            R"(
+    primitiveIdFlat = primId;
+)"
+#endif
+            R"(
     gl_PointSize = pointSize;
   }
 )";
diff --git a/source/MRViewer/MRShaderBlocks.cpp b/source/MRViewer/MRShaderBlocks.cpp
index f15cd093d208..2e182fa07fd0 100644
--- a/source/MRViewer/MRShaderBlocks.cpp
+++ b/source/MRViewer/MRShaderBlocks.cpp
@@ -22,11 +22,18 @@ std::string getPickerFragmentShader( bool points, bool cornerMode )
   out highp uvec4 color;
 )";
 
+    // outside corner mode the id arrives in a flat integer varying: gl_PrimitiveID came back
+    // as garbage under llvmpipe 21.1.8 / Mesa 26.0.8. Declared only where read, so the pickers
+    // that stay in corner mode keep linking against vertex shaders without it.
     const std::string primId =
         cornerMode ? R"(
     uint primitiveId = ( uint(primitiveIdf1) << 20u ) + uint(primitiveIdf0);
 )" : R"(
-    uint primitiveId = uint(gl_PrimitiveID);
+    uint primitiveId = primitiveIdFlat;
+)";
+
+    const std::string idDecl = cornerMode ? "" : R"(
+  flat in uint primitiveIdFlat;
 )";
 
     const std::string tail = R"(
@@ -39,6 +46,7 @@ std::string getPickerFragmentShader( bool points, bool cornerMode )
 
     return
         head +
+        idDecl +
         getShaderMainBeginBlock( false ) +
         ( points ? getFragmentShaderPointSizeBlock() : R"()" ) +
         getFragmentShaderClippingBlock() +