The European Union's data protection watchdog is worried that a new transatlantic data-transfer pact agreed in February doesn't go far enough, calling for a "more robust and sustainable solution."

The pact, known as the EU-U.S. Privacy Shield, seeks to protect European citizens when their personal data is transferred to the U.S. for commercial purposes.

It is meant to replace the former 15-year-old Safe Harbor pact struck down by the EU's highest court last October. The came stemmed from a complaint brought by an Austrian privacy campaigner against Facebook (FB) - Get Report .

Among other things the new accord would impose stronger obligations on companies, including sanctions or exclusion if they do not comply. It would also impose safeguards against mass surveillance by U.S. authorities, brought to light by the Edward Snowden revelations.

In the EU, the legal texts implementing the EU-U.S. Privacy Shield still need to be finalized, which an EC spokesman told The Street is expected in late June or early July.

In the meantime, some policymakers are calling for tweaks to the February draft.

Giovanni Buttarelli, the European Data Protection Supervisor, said in a statement Monday that while he appreciates efforts to develop a solution to replace Safe Harbor, "the Privacy Shield as it stands is not robust enough to withstand future legal scrutiny."

Specifically, he urged adequate protection against indiscriminate surveillance as well as obligations on oversight, transparency, redress and data protection right.

He also said it was time to craft a longer-term solution in the transatlantic dialog.

Buttarelli is a member of a data protection working group that voiced its concerns about the accord last month. They said that while the Privacy Shield offers "major improvements" over Safe Harbor, they remain worried that some key data protection principles outlined in European law are not adequately addressed.

Vera Jourova, the European Commissioner for Justice, Consumers and Gender Equality, said last week that the EC is "working on the more critical aspects" of the draft agreement, in discussions with the U.S. government.

One of the points under discussion is clarifying the independence and functioning of the newly created Ombudsperson mechanism to handle and solve complaints or inquiries raised by Europeans under the new rules, she said.

(Facebook is held in Jim Cramer's charitable trust Action Alerts PLUS. See all of his holdings here.)