"Round up the usual suspects." That famous line from "Casablanca" neatly sums up the regulatory attitude toward the banking industry in the aftermath of the financial crisis. In their understandable eagerness to show a toughened regulatory posture to a disillusioned public, regulators cast a wide supervisory net. In the process, they failed to sufficiently differentiate regional and community banks — bread-and-butter lenders that for the most part remained healthy and profitable before, during and after the crisis — from the main actors in the subprime debacle: the originators of toxic mortgages and the big firms that structured all those exotic securities and derivatives products on top of them.

Indeed, notwithstanding the protests of some Federal Deposit Insurance Corp. board members, the regulators' first rulemaking to strengthen capital standards primarily affected community and regional banks. Tougher capital rules for the largest systemic institutions were not completed until last year. Similarly, complex, labor-intensive "stress tests" were imposed on the smaller, traditional lenders, using supervisory approaches that were cut and pasted from the elaborate procedures developed for the largest institutions.  Banks as small as $10 billion had to contend with an expensive laundry list of new processes and systems, committees and compliance staff. Regional banks over $50 billion fared even worse as supervisors indiscriminately lumped smaller institutions like M&T and Discover with complex behemoths such as Citigroup and JPMorgan Chase.

The Dodd-Frank Act authorized all of this, while at the same time explicitly granting regulators authority to set higher thresholds for "enhanced" supervisory tools and to tailor those tools to the risks posed by individual institutions. Unfortunately, the banking agencies failed to effectively use this discretion until recently when Federal Reserve Chair Janet Yellen announced that the central bank would (finally) start easing up on institutions with assets of less than $250 billion. This may be too little, too late.

A "Fed-up" Senate Banking Committee Chairman Richard Shelby continues to push a bill that would make it difficult for the Fed to impose tougher supervisory measures on any banking holding company with less than $500 billion in assets.  He would accomplish this by forcing the agency to humbly seek approval of the Financial Stability Oversight Council before determining that banks of this size are "systemic" and thus deserving of tougher supervision. Critics of the bill have questioned whether the FSOC would ever approve a banking organization of less than $500 billion for enhanced oversight, as the FSOC is composed of a large number of agency heads with differing viewpoints and their decision-making is not always (ahem) timely. Critics have also argued that a threshold of $500 billion for automatic "systemic" designation is far too high.

Are these fears founded? In my view, focusing on the dollar trigger for enhanced supervision is misplaced. Size is not always a good proxy for systemic risk. Even a very large bank may not be systemic if it follows a traditional business model of taking deposits and making loans. At the same time, a bank with a few hundred billion in assets may pose systemic risk if it relies on unstable funding, holds volatile assets and is heavily interconnected with other financial firms through, for instance, derivatives dealing, clearing or custodial services. Note that the London arm of AIG that wreaked such havoc in the CDS market had, on a stand-alone basis, assets far less than $500 billion.

Thus significantly raising the automatic threshold for systemic status should not be problematic if regulators continued to have authority to impose heightened standards on smaller bank holding companies they believe to pose systemic threat. To be sure, some required process around who the Fed designates as systemic and why would be justified given post-crisis over-reach. For instance, the Fed could be required to issue a notice explaining why it views a BHC as systemic and provide the BHC with the right to respond. But the systemic designation authority for BHCs should remain with the Fed in consultation with other bank regulators. Bank holding companies are in the safety net. By definition, they enjoy explicit government support through their FDIC-insured subsidiaries and access to the Fed's lending facilities.

FSOC "systemic" designation for nonbanks, such as insurance companies or securities firms, is appropriate as they have not voluntarily submitted to prudential supervision as has a BHC, and the FSOC includes nonbank regulators who have helpful expertise in designating nonbank firms. But most members of the FSOC are not bank supervisors and have no institutional mandate to protect the safety net. Empowering that group to insert itself into the supervisory discretion of the banking agencies would open the door to mischievous lobbying that could impede effective and timely oversight of institutions which are truly systemic.

With the full faith and credit of the government standing behind roughly $7 trillion in insured deposits, banking supervisors need wide latitude to protect against undue risk-taking by insured banks and their holding companies. Though the Shelby bill is not intended to weaken bank supervisors' longstanding safety and soundness powers, difficulties in differentiating between an insured bank and the holding company of which it is a part will undoubtedly have a chilling effect on supervisors' willingness to imposed heightened standards on any part of a banking organization with less than $500 billion in assets. Make no mistake — as we saw during the crisis, activities of bank holding companies can pose significant risks to their insured banks.

Similarly, to protect against unnecessary losses, banking supervisors need wide latitude to require resolution planning among FDIC insured institutions, another component of "enhanced" supervision. Though some resolution planning requirements may have gone too far, others are simply a matter of good management, such as current records on insured and uninsured depositors, counterparties, major credit exposures and organizational structure.

The Shelby bill has many useful provisions: eliminating statutory stress tests for BHCs with less than $50 billion; making the $50 billion threshold an automatic "out" from systemic status; clarifying the inapplicability of the Volcker Rule to most community banks; and mandating a short form call report would all provide helpful relief without compromising supervisory tools necessary for financial stability. Of course, it would be even better if Congress would also consider measures to strengthen the rules such as the bill introduced by Sens. Sherrod Brown, D-Ohio, and David Vitter, R-La., to significantly limit leverage at the largest, riskiest firms.

That said, with further refinements, the Shelby bill could help redirect more intensive government oversight to the banks that truly pose systemic risk, while providing breathing room to traditional lenders to make loans, particularly small-business loans, the lifeblood of economic development and job creation. The combination of compressed margins from near-zero interest rates and increased regulatory burdens has disproportionately affected traditional lenders. It's time to let them give greater attention to their basic function: providing credit to the real economy.

Sheila Bair is a former chairman of the FDIC and now serves as president of Washington College in Maryland. The views expressed are her own.