diff --git a/egs/librispeech/ASR/pruned_transducer_stateless7/optim.py b/egs/librispeech/ASR/pruned_transducer_stateless7/optim.py
index a8a0a05b0..bd0435db5 100644
--- a/egs/librispeech/ASR/pruned_transducer_stateless7/optim.py
+++ b/egs/librispeech/ASR/pruned_transducer_stateless7/optim.py
@@ -419,7 +419,7 @@ param_rms_smooth1: Smoothing proportion for parameter matrix, if assumed rank of
                 # rate matrices at most every other time we reach here, and
                 # less frequently than that later in training.
                 #self._update_param_scales(group, p, state, P_proj)
-                self._update_param_scales_simple(group, p, state, P_proj)
+                #self._update_param_scales_simple(group, p, state, P_proj)
 
                 # We won't be doing this any more.
                 #self._diagonalize_grad_cov(group, p, state)
@@ -608,6 +608,7 @@ param_rms_smooth1: Smoothing proportion for parameter matrix, if assumed rank of
                 logging.info(f"step={step}, dim={dim}, size={size}, scale min,max,mean={scale_min,scale_max,scale_mean}")
 
             Q *= this_P_proj.sqrt()
+            logging.info(f"Q rms = {(Q**2).mean().sqrt()}, abs-rms = {Q.abs().mean()}")
 
     def _update_param_scales(self,
                              group: dict,
@@ -950,13 +951,42 @@ param_rms_smooth1: Smoothing proportion for parameter matrix, if assumed rank of
             # this_P_proj shape: (batch_size, num_blocks, block_size)
             this_P_proj = _diag(torch.matmul(U_prod, torch.matmul(P_prime, U_prod.transpose(2, 3))))
             P_proj[dim] =  this_P_proj.clone().reshape(batch_size, size)
+
+            simple_update = True
+            if simple_update:
+                # normalize the scales in a way that preserves the Frobenius norm of the
+                # projected parameter deltas
+                P_rms = this_P_proj.clone()
+                P_rms = P_rms / _mean(P_rms, exclude_dims=[0], keepdim=True)
+                P_rms_compare = this_P_proj.clone()
+                P_rms_compare /= _mean(P_rms_compare, exclude_dims=[0], keepdim=True)
+
+                mean_diff = (P_rms - P_rms_compare)
+                if True:
+                    ratio = mean_diff.abs().sum() / P_rms.abs().sum()
+                    logging.info(f"ratio for division is {ratio}, shapes are {P_rms.shape}, {P_rms_compare.shape}")
+                    if ratio > 1.0e-10:
+                        logging.warn(f"P_rms={P_rms}, P_rms_compare={P_rms_compare}")
+                scale = P_rms.unsqueeze(-1).sqrt()
+                Q *= scale
+                logging.info(f"Q rms = {(Q**2).mean().sqrt()}, abs-rms = {Q.abs().mean()}")
+
+                # no iterative stuff, just use sqrt(P_proj) as scale on Q.  If this is False, we need to
+                # call self._update_param_scales(...) from the calling function.
+                if True:
+                    # debug output
+                    step = state["step"]
+                    scale_min, scale_max, scale_mean = scale.min().item(), scale.max().item(), scale.mean().item()
+                    logging.info(f"step={step}, dim={dim}, size={size}, scale min,max,mean={scale_min,scale_max,scale_mean}")
             if True:
+                # debug output
                 this_P_proj_unsmoothed = _diag(torch.matmul(U_prod, torch.matmul(P_prime_unsmoothed,
                                                                                  U_prod.transpose(2, 3))))
                 this_P_proj_unsmoothed = this_P_proj_unsmoothed.clone().reshape(batch_size, size)
                 skip = 10 if P_proj[dim].shape[-1] > 40 else 1
                 logging.info(f"dim={dim}, diag of P_proj is: {P_proj[dim][0,::skip]}, diag of unsmoothed P_proj is: {this_P_proj_unsmoothed[0,::skip]}")
 
+        # P_proj won't be needed if simple_update == True.
         return P_proj