The income tax provision differed from the amounts computed by applying the U.S. federal income tax rate of 21% to income before income tax for the reasons set forth below (dollars in thousands):


	Three months ended June 30,
	2025				2024
U.S. federal statutory tax rate	$	375	21.0	%	$	420	21.0	%
State income taxes, net of federal benefit	17		1.0	%	15		0.7	%
Non-U.S. income taxed at different rates	(45)		(2.5)	%	(61)		(3.1)	%
Increase (reduction) in tax expense related to stock-based awards	(188)		(10.5)	%	16		0.8	%
Change in valuation allowance	(416)		(23.3)	%	(387)		(19.4)	%
Non-deductible expenses	274		15.3	%	12		0.6	%

Income tax expense and effective rate	$	17	1.0	%	$	15	0.6	%


	Six months ended June 30,
		2025				2024
U.S. federal statutory tax rate		$	1,518	21.0	%	$	796	21.0	%
State income taxes, net of federal benefit		81		1.1	%	256		6.8	%
Non-U.S. income taxed at different rates		(120)		(1.7)	%	(153)		(4.1)	%
Increase (reduction) in tax expense related to stock-based awards		(190)		(2.6)	%	39		1.0	%
Change in valuation allowance		(1,642)		(22.7)	%	(724)		(19.1)	%
Non-deductible expenses		434		6.0	%	43		1.1	%

Income tax expense and effective rate		$	81	1.1	%	$	257	6.7	%